The Comprehensive LATEX Symbol List

Home , Alphabetical order, Ampersand, Arrows (Unicode block), Arrow (symbol), Astronomical symbols, Backslash

Scott Pakin ∗ 8 October 2002

Abstract This document lists 2590 symbols and the corresponding LATEX commands that produce them. Some of these symbols are guaranteed to be available in every LATEX 2ε system; others require fonts and packages that may not accompany a given distribution and that therefore need to be installed. All of the fonts and packages used to prepare this document—as well as this document itself—are freely available from the Comprehensive TEX Archive Network (http://www.ctan.org).

Contents

1 Introduction 6 1.1 Document Usage ...... 6 1.2 Frequently Requested Symbols ...... 6

2 Body-text symbols 7 Table 1: LATEX 2ε Escapable “Special” Characters ...... 7 Table 2: LATEX 2ε Commands Defined to Work in Both Math and Text Mode ...... 7 Table 3: Predefined LATEX 2ε Text-Mode Commands ...... 7 Table 4: Non-ASCII Letters (Excluding Accented Letters) ...... 7 Table 5: Letters Used to Typeset African Languages ...... 8 Table 6: Punctuation Marks Not Found in OT1 ...... 8 Table 7: pifont Decorative Punctuation Marks ...... 8 Table 8: wasysym Phonetic Symbols ...... 8 Table 9: tipa Phonetic Symbols ...... 8 Table 10: wsuipa Phonetic Symbols ...... 9 Table 11: Text-Mode Accents ...... 10 Table 12: tipa Text-Mode Accents ...... 11 Table 13: wsuipa Text-Mode Accents ...... 12 Table 14: wsuipa Diacritics ...... 12 Table 15: textcomp Diacritics ...... 12 Table 16: textcomp Currency Symbols ...... 12 Table 17: marvosym Currency Symbols ...... 13 Table 18: wasysym Currency Symbols ...... 13 Table 19: eurosym Euro Signs ...... 13 Table 20: textcomp Legal Symbols ...... 13 Table 21: textcomp Old-Style Numerals ...... 13 Table 22: Miscellaneous textcomp Symbols ...... 14 Table 23: Miscellaneous wasysym Text-Mode Symbols ...... 14 Table 24: AMS Commands Defined to Work in Both Math and Text Mode ...... 14

∗The original version of this document was written by David Carlisle, with several additional tables provided by Alexander Holt. See Section 7.5 on page 54 for more information about who did what.

1 3 Mathematical symbols 15 Table 25: Binary Operators ...... 15 Table 26: AMS Binary Operators ...... 15 Table 27: stmaryrd Binary Operators ...... 16 Table 28: wasysym Binary Operators ...... 16 Table 29: txfonts/pxfonts Binary Operators ...... 16 Table 30: mathabx Binary Operators ...... 17 Table 31: ulsy Geometric Binary Operators ...... 17 Table 32: mathabx Geometric Binary Operators ...... 17 Table 33: Variable-sized Math Operators ...... 17 Table 34: AMS Variable-sized Math Operators ...... 18 Table 35: stmaryrd Variable-sized Math Operators ...... 18 Table 36: wasysym Variable-sized Math Operators ...... 18 Table 37: mathabx Variable-sized Math Operators ...... 18 Table 38: txfonts/pxfonts Variable-sized Math Operators ...... 19 Table 39: esint Variable-sized Math Operators ...... 19 Table 40: Binary Relations ...... 20 Table 41: AMS Binary Relations ...... 20 Table 42: AMS Negated Binary Relations ...... 20 Table 43: stmaryrd Binary Relations ...... 20 Table 44: wasysym Binary Relations ...... 20 Table 45: txfonts/pxfonts Binary Relations ...... 21 Table 46: txfonts/pxfonts Negated Binary Relations ...... 21 Table 47: mathabx Binary Relations ...... 21 Table 48: mathabx Negated Binary Relations ...... 22 Table 49: Subset and Superset Relations ...... 22 Table 50: AMS Subset and Superset Relations ...... 22 Table 51: stmaryrd Subset and Superset Relations ...... 22 Table 52: wasysym Subset and Superset Relations ...... 22 Table 53: txfonts/pxfonts Subset and Superset Relations ...... 23 Table 54: mathabx Subset and Superset Relations ...... 23 Table 55: Inequalities ...... 23 Table 56: AMS Inequalities ...... 23 Table 57: wasysym Inequalities ...... 23 Table 58: txfonts/pxfonts Inequalities ...... 24 Table 59: mathabx Inequalities ...... 24 Table 60: AMS Triangle Relations ...... 24 Table 61: stmaryrd Triangle Relations ...... 24 Table 62: mathabx Triangle Relations ...... 24 Table 63: Arrows ...... 25 Table 64: Harpoons ...... 25 Table 65: textcomp Text-Mode Arrows ...... 25 Table 66: AMS Arrows...... 25 Table 67: AMS Negated Arrows ...... 25 Table 68: AMS Harpoons ...... 25 Table 69: stmaryrd Arrows ...... 26 Table 70: txfonts/pxfonts Arrows ...... 26 Table 71: mathabx Arrows ...... 26 Table 72: mathabx Negated Arrows ...... 26 Table 73: mathabx Harpoons ...... 27 Table 74: ulsy Contradiction Symbols ...... 27 Table 75: Extension Characters ...... 27 Table 76: stmaryrd Extension Characters ...... 27 Table 77: txfonts/pxfonts Extension Characters ...... 27 Table 78: mathabx Extension Characters ...... 27 Table 79: Log-like Symbols ...... 27 Table 80: AMS Log-like Symbols ...... 28

2 Table 81: Greek Letters ...... 28 Table 82: AMS Greek Letters ...... 28 Table 83: txfonts/pxfonts Upright Greek Letters ...... 28 Table 84: txfonts/pxfonts Variant Latin Letters ...... 28 Table 85: AMS Hebrew Letters ...... 29 Table 86: Letter-like Symbols ...... 29 Table 87: AMS Letter-like Symbols ...... 29 Table 88: txfonts/pxfonts Letter-like Symbols ...... 29 Table 89: mathabx Letter-like Symbols ...... 29 Table 90: AMS Delimiters ...... 29 Table 91: stmaryrd Delimiters ...... 29 Table 92: mathabx Delimiters ...... 29 Table 93: Variable-sized Delimiters ...... 30 Table 94: Large, Variable-Sized Delimiters ...... 30 Table 95: Variable-Sized stmaryrd Delimiters ...... 30 Table 96: mathabx Variable-Sized Delimiters ...... 30 Table 97: textcomp Text-Mode Delimiters ...... 31 Table 98: Math-Mode Accents ...... 31 Table 99: AMS Math-Mode Accents ...... 31 Table 100: yhmath Math-Mode Accents ...... 31 Table 101: Extensible Accents ...... 31 Table 102: yhmath Extensible Accents ...... 31 Table 103: AMS Extensible Accents ...... 32 Table 104: mathabx Extensible Accents ...... 32 Table 105: esvect Extensible Accents ...... 32 Table 106: Dots ...... 33 Table 107: AMS Dots ...... 33 Table 108: yhmath Dots ...... 33 Table 109: Miscellaneous LATEX 2ε Symbols ...... 33 Table 110: Miscellaneous AMS Symbols ...... 33 Table 111: Miscellaneous wasysym Symbols ...... 34 Table 112: Miscellaneous txfonts/pxfonts Symbols ...... 34 Table 113: Miscellaneous mathabx Symbols ...... 34 Table 114: Miscellaneous textcomp Text-Mode Math Symbols ...... 34 Table 115: mathcomp Math Symbols ...... 34 Table 116: mathabx Mayan Digits ...... 34 Table 117: marvosym Math Symbols ...... 34 Table 118: Math Alphabets ...... 35

4 Science and technology symbols 36 Table 119: wasysym Electrical and Physical Symbols ...... 36 Table 120: ifsym Pulse Diagram Symbols ...... 36 Table 121: ar Aspect Ratio Symbol ...... 36 Table 122: textcomp Text-Mode Science and Engineering Symbols ...... 36 Table 123: wasysym Astronomical Symbols ...... 36 Table 124: marvosym Astronomical Symbols ...... 36 Table 125: mathabx Astronomical Symbols ...... 37 Table 126: wasysym Astrological Symbols ...... 37 Table 127: marvosym Astrological Symbols ...... 37 Table 128: mathabx Astrological Symbols ...... 37 Table 129: wasysym APL Symbols ...... 37 Table 130: wasysym APL Modiﬁers ...... 37 Table 131: marvosym Computer Hardware Symbols ...... 37 Table 132: ascii Control Characters (IBM) ...... 38 Table 133: marvosym Communication Symbols ...... 38 Table 134: marvosym Engineering Symbols ...... 38 Table 135: wasysym Biological Symbols ...... 38 Table 136: marvosym Biological Symbols ...... 38

3 Table 137: marvosym Safety-Related Symbols ...... 38

5 Dingbats 39 Table 138: bbding Arrows ...... 39 Table 139: pifont Arrows...... 39 Table 140: marvosym Scissors ...... 39 Table 141: bbding Scissors ...... 39 Table 142: pifont Scissors ...... 39 Table 143: dingbat Pencils ...... 39 Table 144: bbding Pencils and Nibs ...... 40 Table 145: pifont Pencils and Nibs ...... 40 Table 146: dingbat Hands ...... 40 Table 147: bbding Hands ...... 40 Table 148: pifont Hands ...... 40 Table 149: bbding Crosses and Plusses ...... 40 Table 150: pifont Crosses and Plusses ...... 40 Table 151: bbding Xs and Check Marks ...... 40 Table 152: pifont Xs and Check Marks ...... 41 Table 153: wasysym Xs and Check Marks ...... 41 Table 154: pifont Circled Numbers ...... 41 Table 155: wasysym Stars ...... 41 Table 156: bbding Stars, Flowers, and Similar Shapes ...... 41 Table 157: pifont Stars, Flowers, and Similar Shapes ...... 42 Table 158: wasysym Geometric Shapes ...... 42 Table 159: ifsym Geometric Shapes ...... 42 Table 160: bbding Geometric Shapes ...... 43 Table 161: pifont Geometric Shapes ...... 43 Table 162: manfnt Dangerous Bend Symbols ...... 43 Table 163: skull Symbols...... 43 Table 164: Non-Mathematical mathabx Symbols ...... 43 Table 165: marvosym Information Symbols ...... 43 Table 166: Miscellaneous dingbat Dingbats ...... 43 Table 167: Miscellaneous bbding Dingbats ...... 44 Table 168: Miscellaneous pifont Dingbats ...... 44

6 Other symbols 45 Table 169: textcomp Genealogical Symbols ...... 45 Table 170: wasysym General Symbols ...... 45 Table 171: wasysym Musical Notes ...... 45 Table 172: wasysym Circles ...... 45 Table 173: Miscellaneous manfnt Symbols ...... 45 Table 174: marvosym Navigation Symbols ...... 46 Table 175: marvosym Laundry Symbols ...... 46 Table 176: Other marvosym Symbols ...... 46 Table 177: ifsym Weather Symbols ...... 46 Table 178: ifsym Alpine Symbols ...... 47 Table 179: ifsym Clocks ...... 47 Table 180: Other ifsym Symbols ...... 47

7 Additional Information 48 7.1 Symbol Name Clashes ...... 48 7.2 Where can I ﬁnd the symbol for ... ?...... 48 7.3 Math-mode spacing ...... 52 7.4 ASCII and Latin 1 quick reference ...... 53 7.5 About this document ...... 54

References 57

4 Index 58

5 1 Introduction

Welcome to the Comprehensive LATEX Symbol List! This document strives to be your primary source of LATEX symbol information: font samples, LATEX commands, packages, usage details, caveats—everything needed to put thousands of diﬀerent symbols at your disposal. All of the fonts covered herein meet the following criteria:

1. They are freely available from the Comprehensive TEX Archive Network (http://www.ctan.org). 2. All of their symbols have LATEX 2ε bindings. That is, a user should be able to access a symbol by name, not just by \charhnumberi.

These are not particularly limiting criteria; the Comprehensive LATEX Symbol List contains samples of 2590 symbols—quite a large number. Some of these symbols are guaranteed to be available in every LATEX 2ε system; others require fonts and packages that may not accompany a given distribution and that therefore need to be installed. See http://www.tex.ac.uk/cgi-bin/texfaq2html?label=instpackages+wherefiles for help with installing new fonts and packages.

1.1 Document Usage Each section of this document contains a number of font tables. Each table shows a set of symbols, with the corresponding LATEX command to the right of each symbol. A table’s caption indicates what package needs to be loaded in order to access that table’s symbols. For example, the symbols in Table 21, “textcomp Old-Style Numerals”, are made available by putting “\usepackage{textcomp}” in your document’s preamble. “AMS” means to use the AMS packages, viz. amssymb and/or amsmath. Notes below a table provide additional information about some or all the symbols in that table. One note that appears a few times in this document, particularly in Section 2, indicates that certain symbols do not exist in the OT1 font encoding (Donald Knuth’s original, 7-bit font encoding, which is the default font encoding for LATEX) and that you should use fontenc to select a diﬀerent encoding, such as T1 (a common 8-bit font encoding). That means that you should put “\usepackage[hencodingi]{fontenc}” in your document’s preamble, where hencodingi is, e.g., T1 or LY1. To limit the change in font encoding to the current group, use “\fontencoding{hencodingi}\selectfont”. Section 7 contains some additional information about the symbols in this document. It shows which symbol names are not unique across packages, gives examples of how to create new symbols out of existing symbols, explains how symbols are spaced in math mode, presents a LATEX ASCII and Latin 1 tables, and provides some information about this document itself. The Comprehensive LATEX Symbol List ends with an index of all the symbols in the document and various additional useful terms.

1.2 Frequently Requested Symbols There are a number of symbols that are requested over and over again on comp.text.tex. If you’re looking for such a symbol the following list will help you ﬁnd it quickly.

, as in “Spaces are significant.” ...... 7 ...... 33 ´ı,`ı,¯ı,ˆı, etc. (versus í, ì, ¯i, and î) ...... 10 °, as in “180°” or “15” ...... 34 ¢ ...... 12 L, F, etc...... 35 e ...... 13 N, Z, R,etc...... 35 ©, ®, and ...... 13 ¯a,´ ê,` etc. (i.e., several accents per character) 52 ...... 14 R − ...... 50 ...... 19 < and > (instead of ¡ and ¿) ...... 53 ...... 20 ∴ ˜ (or ∼) ...... 53 B and F ...... 21

6 2 Body-text symbols

This section lists symbols that are intended for use in running text, such as punctuation marks, accents, ligatures, and currency symbols.

Table 1: LATEX 2ε Escapable “Special” Characters $ \$ % \% \_ } \} & \& # \# { \{

Table 2: LATEX 2ε Commands Deﬁned to Work in Both Math and Text Mode $ \$ \_ \ddag { \{ ¶ \P Oc © \copyright ... \dots } \} § \S \dag £ \pounds

Where two symbols are present, the left one is the “faked” symbol that LATEX 2ε provides by default, and the right one is the “true” symbol that textcomp makes available.

Table 3: Predeﬁned LATEX 2ε Text-Mode Commands ˆ \textasciicircum < \textless ˜ \textasciitilde a ª \textordfeminine * \textasteriskcentered o º \textordmasculine \ \textbackslash ¶ \textparagraph | \textbar · \textperiodcentered { \textbraceleft ¿ \textquestiondown } \textbraceright “ \textquotedblleft \textbullet ” \textquotedblright Oc © \textcopyright ‘ \textquoteleft \textdagger ’ \textquoteright \textdaggerdbl Or ® \textregistered $ \textdollar § \textsection ... \textellipsis £ \textsterling — \textemdash TM \texttrademark – \textendash \textunderscore ¡ \textexclamdown \textvisiblespace > \textgreater

Where two symbols are present, the left one is the “faked” symbol that LATEX 2ε provides by default, and the right one is the “true” symbol that textcomp makes available.

Table 4: Non-ASCII Letters (Excluding Accented Letters) ˚a \aa Ð \DH∗ L \L ø \o ß \ss A˚ \AA ð \dh∗ l \l Ø \O SS \SS Æ \AE Ð \DJ∗ \NG∗ Œ \OE Þ \TH∗ æ \ae \dj∗ \ng∗ œ \oe þ \th∗

∗ Not available in the OT1 font encoding. Use the fontenc package to select an alternate font encoding, such as T1.

7 Table 5: Letters Used to Typeset African Languages Ð \B{D} ° \m{c} ¤ \m{f} ¨ \m{k} » \M{t} \m{Z} \B{d} \m{D} \m{F} \m{N} \M{T} Â \T{E} \B{H} ð \M{d} \m{G} \m{n} º \m{t} â \T{e} § \B{h} Ð \M{D} ¦ \m{g} ª \m{o} \m{T} Å \T{O} · \B{t} ¡ \m{d} À \m{I} \m{O} ® \m{u}∗ å \T{o} \B{T} \m{E} à \m{i} \m{P} \m{U}∗ \m{b} ¢ \m{e} \m{J} ± \m{p} \m{Y} \m{B} \M{E} © \m{j} ¬ \m{s} ¯ \m{y} \m{C} £ \M{e} \m{K} \m{S} ¶ \m{z}

These characters all need the T4 font encoding, which is provided by the fc package.

∗ \m{v} and \m{V} are synonyms for \m{u} and \m{U}.

Table 6: Punctuation Marks Not Found in OT1 \guillemotleft \guilsinglleft \quotedblbase " \textquotedbl \guillemotright \guilsinglright \quotesinglbase

To get these symbols, use the fontenc package to select an alternate font encoding, such as T1.

Table 7: pifont Decorative Punctuation Marks ❛ \ding{123} ❝ \ding{125} ❡ \ding{161} ❣ \ding{163} ❜ \ding{124} ❞ \ding{126} ❢ \ding{162}

Table 8: wasysym Phonetic Symbols D \DH \dh \openo \Thorn k \inve l \thorn Þ U þ

Table 9: tipa Phonetic Symbols

È \textbabygamma P \textglotstop ï \textrtailn b \textbarb ; \texthalflength ó \textrtailr c \textbarc » \texthardsign ù \textrtails d \textbard # \texthooktop ú \textrtailt é \textbardotlessj á \texthtb ü \textrtailz g \textbarg ê \texthtbardotlessj $ \textrthook Ü \textbarglotstop Á \texthtc À \textsca 1 \textbari â \texthtd à \textscb

(continued on next page)

8 (continued from previous page)

ª \textbarl ä \texthtg ¤ \textsce 8 \textbaro H \texthth å \textscg Ý \textbarrevglotstop Ê \texththeng Ë \textsch 0 \textbaru Î \texthtk @ \textschwa ì \textbeltl Ò \texthtp I \textsci B \textbeta Ó \texthtq ¨ \textscj ò \textbullseye £ \texthtrtaild Ï \textscl \textceltpal É \texthtscg ð \textscn X \textchi Ö \texthtt × \textscoelig Å \textcloseepsilon ÿ \texthvlig ± \textscomega Ñ \textcloseomega Û \textinvglotstop ö \textscr Æ \textcloserevepsilon K \textinvscr A \textscripta Þ \textcommatailz Ì \textiota g \textscriptg ^ \textcorner « \textlambda V \textscriptv \textcrb : \textlengthmark Ú \textscu ¡ \textcrd ³ \textlhookt Y \textscy g \textcrg ¦ \textlhtlongi \textsecstress è \textcrh ¶ \textlhtlongy º \textsoftsign Û \textcrinvglotstop Ô \textlonglegr Â \textstretchc ¬ \textcrlambda ½ \textlptr tC \texttctclig 2 \textcrtwo M \textltailm Ù \textteshlig C \textctc ñ \textltailn T \texttheta ¢ \textctd ë \textltilde þ \textthorn ¢ý \textctdctzlig Ð \textlyoghlig ¿ \texttoneletterstem ² \textctesh Í \textObardotlessj µ \texttslig J \textctj \textOlyoghlig 5 \textturna ® \textctn ° \textomega ¯ \textturncelig ´ \textctt _ \textopencorner 4 \textturnh ´C \textcttctclig O \textopeno © \textturnk ¸ \textctyogh % \textpalhook Õ \textturnlonglegr ý \textctz F \textphi W \textturnm dý \textdctzlig | \textpipe î \textturnmrleg S \textdoublebaresh " \textprimstress ô \textturnr } \textdoublebarpipe ¼ \textraiseglotstop õ \textturnrrtail =/ \textdoublebarslash § \textraisevibyi 6 \textturnscripta { \textdoublepipe 7 \textramshorns Ø \textturnt \textdoublevertline \ \textrevapostrophe 2 \textturnv \textdownstep 9 \textreve û \textturnw Ã \textdyoghlig 3 \textrevepsilon L \textturny dz \textdzlig Q \textrevglotstop U \textupsilon E \textepsilon ¹ \textrevyogh \textupstep S \textesh Ç \textrhookrevepsilon \textvertline R \textfishhookr Ä \textrhookschwa § \textvibyi ¥ \textg ~ \textrhoticity · \textvibyy G \textgamma ¾ \textrptr ß \textwynn \textglobfall ã \textrtaild Z \textyogh \textglobrise í \textrtaill

tipa deﬁnes shortcut characters for many of the above. It also deﬁnes a command \tone for denoting tone letters (pitches). See the tipa documentation for more information.

9 Table 10: wsuipa Phonetic Symbols

! \babygamma 8 \eng 4 \labdentalnas \schwa ¦ \barb \er / \latfric * \sci \bard M \esh 6 \legm : \scn ' \bari \eth E \legr J \scr . \barl D \flapr 1 \lz ¡ \scripta < \baro b \glotstop ¢ \nialpha \scriptg A \barp ¨ \hookb © \nibeta Y \scriptv + \barsci \hookd [ \nichi W \scu X \barscu \hookg \niepsilon ] \scy T \baru $ \hookh \nigamma § \slashb ; \clickb % \hookheng ) \niiota \slashc \clickc \hookrevepsilon 2 \nilambda \slashd R \clickt " \hv > \niomega U \slashu ? \closedniomega \inva C \niphi \taild \closedrevepsilon , \invf O \nisigma H \tailinvr ¥ \crossb d \invglotstop S \nitheta 0 \taill \crossd & \invh V \niupsilon 9 \tailn # \crossh I \invlegr 7 \nj F \tailr 3 \crossnilambda 5 \invm @ \oo L \tails \curlyc G \invr = \openo P \tailt N \curlyesh K \invscr \reve _ \tailz a \curlyyogh £ \invscripta f \reveject Q \tesh ^ \curlyz ¤ \invv \revepsilon B \thorn ( \dlbari Z \invw c \revglotstop - \tildel \dz \ \invy \scd ` \yogh e \ejective \ipagamma \scg

Table 11: Text-Mode Accents Aä¨ \"{A}\"{a} Aà` \‘{A}\‘{a} A˝a˝ \H{A}\H{a} A˘a˘ \u{A}\u{a} Aá´ \’{A}\’{a} Aa \b{A}\b{a} ¡ \k{A}\k{a}† Aˇaˇ \v{A}\v{a} ¯¯ A˙a˙ \.{A}\.{a} A¸¸a \c{A}\c{a} A˚a˚ \r{A}\r{a} Aã˜ \~{A}\~{a} A¯a¯ \={A}\={a} A. a. \d{A}\d{a} Aa \t{A}\t{a} Aâˆ \^{A}\^{a} Aa \G{A}\G{a}‡ A¼a¼ \U{A}\U{a}‡

Aa \newtie{A}\newtie{a}∗ OA Oa \textcircled{A}\textcircled{a}

∗ Requires the textcomp package. † Not available in the OT1 font encoding. Use the fontenc package to select an alternate font encoding, such as T1. ‡ Requires the T4 font encoding, provided by the fc package.

Also note the existence of \i and \j, which produce dotless versions of “i” and “j” (viz., “ı” and “”). These are useful when the accent is supposed to replace the dot. For example, “na\"{\i}ve” produces a correct “na¨ıve”, while “na\"{i}ve” would yield the rather odd-looking “na¨ive”. (“na\"{i}ve” does work in encodings other than OT1, however.)

10 Table 12: tipa Text-Mode Accents ¡ A©a©¡ \textacutemacron{A}\textacutemacron{a} ¡ A§a§¡ \textacutewedge{A}\textacutewedge{a} A a \textadvancing{A}\textadvancing{a}

A¨a¨ \textdotbreve{A}\textdotbreve{a}

A¨a¨ \textdotbreve{A}\textdotbreve{a} A a \textdoublegrave{A}\textdoublegrave{a} Aa \textdoublevbaraccent{A}\textdoublevbaraccent{a} Aa \textgravecircum{A}\textgravecircum{a} Aa \textgravedot{A}\textgravedot{a}

A©a© \textgravemacron{A}\textgravemacron{a} Aa \textgravemid{A}\textgravemid{a} Aa \textinvsubbridge{A}\textinvsubbridge{a} A a \textlowering{A}\textlowering{a} Aa \textmidacute{A}\textmidacute{a} Aa \textovercross{A}\textovercross{a} Aa \textoverw{A}\textoverw{a} A a \textpolhook{A}\textpolhook{a} A a \textraising{A}\textraising{a} A a \textretracting{A}\textretracting{a} ¦ A©¦a© \textringmacron{A}\textringmacron{a} Aa \textroundcap{A}\textroundcap{a} Aa \textseagull{A}\textseagull{a} Aa \textsubacute{A}\textsubacute{a} Aa \textsubarch{A}\textsubarch{a} Aa ©© \textsubbar{A}\textsubbar{a} Aa \textsubbridge{A}\textsubbridge{a} Aa \textsubcircum{A}\textsubcircum{a} ¢¢ Aa \textsubdot{A}\textsubdot{a}

Aa \textsubgrave{A}\textsubgrave{a} A a \textsublhalfring{A}\textsublhalfring{a} A a \textsubplus{A}\textsubplus{a} A a \textsubrhalfring{A}\textsubrhalfring{a} Aa \textsubring{A}\textsubring{a} ¦¦ Aa \textsubsquare{A}\textsubsquare{a} Aa \textsubtilde{A}\textsubtilde{a} ££ Aa \textsubumlaut{A}\textsubumlaut{a} ¤¤ Aa \textsubw{A}\textsubw{a}

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11 (continued from previous page)

Aa \textsubwedge{A}\textsubwedge{a} §§ A&&a \textsuperimposetilde{A}\textsuperimposetilde{a} Aa \textsyllabic{A}\textsyllabic{a} £" " A a£ \texttildedot{A}\texttildedot{a} >> Aa \texttoptiebar{A}\texttoptiebar{a} Aa \textvbaraccent{A}\textvbaraccent{a}

tipa deﬁnes shortcut sequences for many of the above. See the tipa documentation for more information.

Table 13: wsuipa Text-Mode Accents Ag ag \dental{A}\dental{a} Aa \underarch{A}\underarch{a}

Table 14: wsuipa Diacritics s \ain v \leftp x \overring h \stress } \underwedge k \corner n \leftt ~ \polishhook j \syllabic t \upp u \downp q \length w \rightp r \underdots l \upt m \downt { \midtilde o \rightt y \underring p \halflength z \open i \secstress | \undertilde

The wsuipa package deﬁnes all of the above as ordinary characters, not as accents. However, it does provide \diatop and \diaunder commands, which are used to compose diacritics with other characters. For example, \diatop[\overring|a] produces “xa”, and \diaunder[\underdots|a] produces “a”.r See the wsuipa documentation for more information.

Table 15: textcomp Diacritics \textacutedbl \textasciicaron ¯ \textasciimacron ´ \textasciiacute ¨ \textasciidieresis \textgravedbl \textasciibreve ` \textasciigrave ~ \texttildelow

The textcomp package deﬁnes all of the above as ordinary characters, not as accents.

Table 16: textcomp Currency Symbols \textbaht $ \textdollar \textguarani \textwon ¢ \textcent \textdollaroldstyle \textlira ¥ \textyen \textcentoldstyle \textdong \textnaira \textcolonmonetary ¿ \texteuro \textpeso ¤ \textcurrency \textflorin £ \textsterling

12 Table 17: marvosym Currency Symbols ¢ \Denarius e \EUR D \EURdig e \EURtm £ \Pfund \Ecommerce d \EURcr c \EURhv ¦ \EyesDollar ¡ \Shilling

The diﬀerent euro signs are meant to be compatible with diﬀerent fonts—Courier (\EURcr), Helvetica (\EURhv), Times (\EURtm), and the marvosym digits listed in Table 117 (\EURdig).

Table 18: wasysym Currency Symbols \cent \currency ¢ ¤

Table 19: eurosym Euro Signs AC \geneuro BC \geneuronarrow C \geneurowide e \officialeuro

\euro is automatically mapped to one of the above—by default, \officialeuro— based on a eurosym package option. See the eurosym documentation for more information. The \geneuro. . . characters are generated from the current body font’s “C” character and therefore may not appear exactly as shown.

Table 20: textcomp Legal Symbols \textcircledP Oc © \textcopyright \textservicemark « \textcopyleft Or ® \textregistered TM \texttrademark

Where two symbols are present, the left one is the “faked” symbol that LATEX 2ε provides by default, and the right one is the “true” symbol that textcomp makes available.

Table 21: textcomp Old-Style Numerals 0 \textzerooldstyle 4 \textfouroldstyle 8 \texteightoldstyle 1 \textoneoldstyle 5 \textfiveoldstyle 9 \textnineoldstyle 2 \texttwooldstyle 6 \textsixoldstyle 3 \textthreeoldstyle 7 \textsevenoldstyle

Rather than use the bulky \textoneoldstyle, \texttwooldstyle, etc. commands shown above, consider using \oldstylenums{...} to typeset an old-style number.

13 Table 22: Miscellaneous textcomp Symbols * \textasteriskcentered \textopenbullet \textbardbl a ª \textordfeminine O \textbigcircle o º \textordmasculine \textblank ¶ \textparagraph ¦ \textbrokenbar · \textperiodcentered \textbullet \textpertenthousand \textdagger \textperthousand \textdaggerdbl \textpilcrow - \textdblhyphen ' \textquotesingle \textdblhyphenchar \textquotestraightbase \textdiscount \textquotestraightdblbase \textestimated \textrecipe \textinterrobang ¸ \textreferencemark \textinterrobangdown § \textsection n \textmusicalnote \textthreequartersemdash \textnumero \texttwelveudash

Where two symbols are present, the left one is the “faked” symbol that LATEX 2ε provides by default, and the right one is the “true” symbol that textcomp makes available.

Table 23: Miscellaneous wasysym Text-Mode Symbols \permil h

Table 24: AMS Commands Deﬁned to Work in Both Math and Text Mode X \checkmark r \circledR z \maltese

14 3 Mathematical symbols

Most, but not all, of the symbols in this section are math-mode only. That is, they yield a “Missing $ inserted” error message if not used within $...$, \[...\], or another math-mode environment. Operators marked as “variable-sized” are taller in displayed formulas, shorter in in-text formulas, and possibly shorter still when used in various levels of superscripts or subscripts. Alphanumeric symbols (e.g., “L ” and “”) are usually produced using one of the math alphabets in Table 118 rather than with an explicit symbol command. Look there ﬁrst if you need a symbol for a transform, number set, or some other alphanumeric. Although there have been many requests on comp.text.tex for a contradiction symbol, the ensuing discussion invariably reveals innumerable ways to represent contradiction in a proof, including “©”(\blitza), “⇒⇐”(\Rightarrow\Leftarrow), “⊥”(\bot), “=”(\nleftrightarrow), and “¸”(\textreferencemark). Because of the lack of notational consensus, it is probably better to spell out “Contradiction!” than to use a symbol for this purpose. Similarly, discussions on comp.text.tex have revealed that there are a variety of ways to indicate the mathematical notion of “is deﬁned as”. Common candidates include “,”(\triangleq), def “≡”(\equiv), “B”(\coloneqq), and “=” (\stackrel{\text{\tiny def}}{=}).

Table 25: Binary Operators q \amalg ∪ \cup ⊕ \oplus × \times ∗ \ast † \dagger \oslash / \triangleleft \bigcirc ‡ \ddagger ⊗ \otimes . \triangleright ∗ 5 \bigtriangledown \diamond ± \pm E \unlhd ∗ ∗ 4 \bigtriangleup ÷ \div B \rhd D \unrhd ∗ • \bullet C \lhd \ \setminus ] \uplus ∩ \cap ∓ \mp u \sqcap ∨ \vee · \cdot \odot t \sqcup ∧ \wedge ◦ \circ \ominus ? \star o \wr

∗ Not predeﬁned in LATEX 2ε. Use one of the packages latexsym, amsfonts, amssymb, txfonts, pxfonts, or wasysym.

Table 26: AMS Binary Operators Z \barwedge } \circledcirc | \intercal \boxdot \circleddash h \leftthreetimes \boxminus d \Cup n \ltimes \boxplus g \curlyvee i \rightthreetimes \boxtimes f \curlywedge o \rtimes e \Cap > \divideontimes r \smallsetminus \centerdot u \dotplus Y \veebar ~ \circledast [ \doublebarwedge

15 Table 27: stmaryrd Binary Operators \baro \interleave \varoast \bbslash 9 \leftslice \varobar \binampersand 2 \merge \varobslash N \bindnasrepma ! \minuso \varocircle iO \boxast \moo \varodot k \boxbar ` \nplus \varogreaterthan \boxbox \obar 5 \varolessthan j \boxbslash : \oblong 4 \varominus \boxcircle @ \obslash \varoplus ; \boxdot \ogreaterthan \varoslash \boxempty = \olessthan \varotimes l \boxslash < \ovee \varovee \curlyveedownarrow > \owedge 6 \varowedge . \curlyveeuparrow ? \rightslice 7 \vartimes / \curlywedgedownarrow 3 \sslash " \Ydown ' \curlywedgeuparrow \talloblong \Yleft & \fatbslash 8 \varbigcirc \Yright ) \fatsemi , \varcurlyvee \Yup # \fatslash \varcurlywedge (

Table 28: wasysym Binary Operators C \lhd \ocircle \RHD D \unrhd \LHD #B \rhd E \unlhd

Table 29: txfonts/pxfonts Binary Operators V \circledbar T \circledwedge \medcirc W \circledbslash M \invamp } \sqcapplus U \circledvee \medbullet | \sqcupplus

16 Table 30: mathabx Binary Operators ¦ \ast N \curlywedge [ \sqcap ¦ \Asterisk £ \divdot \ \sqcup X \barwedge \divideontimes ^ \sqdoublecap \bigstar ¡ \dotdiv _ \sqdoublecup \bigvarstar \dotplus ¥ \square \blackdiamond ¢ \dottimes ] \squplus X \cap Z \doublebarwedge ¤ \udot ¨ \circplus \ \doublecap Z \uplus § \coasterisk ] \doublecup \varstar § \coAsterisk \ltimes _ \vee \convolution © \pluscirc Y \veebar Y \cup \rtimes [ \veedoublebar O \curlyvee \sqbullet ^ \wedge

Many of the above glyphs go by multiple names. \centerdot is equivalent to \sqbullet, and \ast is equivalent to *. \asterisk produces the same glyph as \ast, but as an ordinary symbol, not a binary operator. Similarly, \bigast produces a large-operator version of the \Asterisk binary operator, and \bigcoast produces a large-operator version of the \coAsterisk binary operator.

Table 31: ulsy Geometric Binary Operators ¨ \odplus

Table 32: mathabx Geometric Binary Operators \blacktriangledown i \boxright a \ominus \blacktriangleleft m \boxslash ` \oplus \blacktriangleright b \boxtimes i \oright \blacktriangleup j \boxtop m \oslash f \boxasterisk o \boxtriangleup b \otimes n \boxbackslash l \boxvoid j \otop k \boxbot f \oasterisk o \otriangleup e \boxcirc n \obackslash l \ovoid g \boxcoasterisk k \obot \smalltriangledown c \boxdiv e \ocirc \smalltriangleleft d \boxdot g \ocoasterisk \smalltriangleright h \boxleft c \odiv \smalltriangleup a \boxminus d \odot ` \boxplus h \oleft

Table 33: Variable-sized Math Operators T \ N O V ^ Q Y \bigcap \bigotimes \bigwedge \prod S [ F G ` a P X \bigcup \bigsqcup \coprod \sum Z J K U ] R \bigodot \biguplus \int I L M W _ H \bigoplus \bigvee \oint

17 Table 34: AMS Variable-sized Math Operators

\idotsint \iiint

' ( \iiiint # $ \iint

% & ! "

Table 35: stmaryrd Variable-sized Math Operators

e m \bigbox g o \biginterleave \bigsqcap

b j \bigcurlyvee \bignplus ` h \bigtriangledown c k \bigcurlywedge f n \bigparallel a i \bigtriangleup

Table 36: wasysym Variable-sized Math Operators

\iiint \oiint \varoint u z $ \iint \varint # r w

! "

Table 37: mathabx Variable-sized Math Operators ¬ Ý ý É é \bigcurlyvee \bigboxslash \bigoright ¦ Ò ò Í í \bigsqcap \bigboxtimes \bigoslash « Ú ú Ê ê \bigcurlywedge \bigboxtop \bigotop Ö ö ß ÿ Ï ï \bigboxasterisk \bigboxtriangleup \bigotriangleup Þ þ Ü ü Ì ì \bigboxbackslash \bigboxvoid \bigovoid Û û ¢ \bigboxbot \bigcomplementop \bigplus Õ õ Æ æ ¨ \bigboxcirc \bigoasterisk \bigsquplus × ÷ Î î ¡ \bigboxcoasterisk \bigobackslash ½ \bigtimes Ó ó Ë ë µ \bigboxdiv \bigobot \iiint ¼ Ô ô Å å ´ \bigboxdot \bigocirc \iint » Ø ø Ç ç ³ \bigboxleft \bigocoasterisk \int ¿ Ñ ñ Ã ã · \bigboxminus \bigodiv \oiint ¾ Ð ð È è ¶ \bigboxplus \bigoleft \oint Ù ù Á á \bigboxright \bigominus

18 Table 38: txfonts/pxfonts Variable-sized Math Operators

\bigsqcapplus \ointclockwise

\bigsqcupplus \ointctrclockwise \fint \sqiiint

> ? \idotsint R S \sqiint

' ( \iiiint P Q \sqint

% & \iiint \varoiiintclockwise

# $ \iint F G \varoiiintctrclockwise

! " \oiiintclockwise N O \varoiintclockwise

L M \oiiintctrclockwise B C \varoiintctrclockwise

D E \oiiint J K \varointclockwise

) * \oiintclockwise - . \varointctrclockwise

H I \oiintctrclockwise + , \varprod

A \oiint @

Table 39: esint Variable-sized Math Operators © \dotsint \ointclockwise \fint \ointctrclockwise ¨ § \iiiint \sqiint ¦ ¥ \iiint \sqint ¤ " £ ! \iint \varoiint & % \landdownint \varointclockwise $ # \landupint \varointctrclockwise

\oiint

19 Table 40: Binary Relations ≈ \approx ≡ \equiv ⊥ \perp ^ \smile \asymp _ \frown ≺ \prec \succ ./ \bowtie Z \Join∗ \preceq \succeq \cong | \mid ∝ \propto ` \vdash a \dashv |= \models ∼ \sim \doteq k \parallel ' \simeq

∗ Not predeﬁned in LATEX 2ε. Use one of the packages latexsym, amsfonts, amssymb, mathabx, txfonts, pxfonts, or wasysym.

Table 41: AMS Binary Relations u \approxeq P \eqcirc v \succapprox \backepsilon ; \fallingdotseq < \succcurlyeq v \backsim ( \multimap % \succsim w \backsimeq t \pitchfork ∴ \therefore ∵ \because w \precapprox ≈ \thickapprox G \between 4 \preccurlyeq ∼ \thicksim m \Bumpeq - \precsim ∝ \varpropto l \bumpeq : \risingdotseq \Vdash $ \circeq p \shortmid \vDash 2 \curlyeqprec q \shortparallel \Vvdash 3 \curlyeqsucc a \smallfrown + \doteqdot ` \smallsmile

Table 42: AMS Negated Binary Relations \ncong / \nshortparallel 3 \nVDash - \nmid / \nsim \precnapprox ∦ \nparallel \nsucc \precnsim ⊀ \nprec \nsucceq \succnapprox \npreceq 2 \nvDash \succnsim . \nshortmid 0 \nvdash

Table 43: stmaryrd Binary Relations \inplus \niplus A B

Table 44: wasysym Binary Relations \invneg { \leadsto \wasypropto Z \Join \logof

20 Table 45: txfonts/pxfonts Binary Relations S \circledgtr X \lJoin ] \opentimes R \circledless \ \lrtimes y \Perp \colonapprox ( \multimap \preceqq \Colonapprox \multimapboth \precneqq D \coloneq \multimapbothvert Y \rJoin H \Coloneq \multimapdot K \strictfi F \Coloneqq \multimapdotboth J \strictif B \coloneqq \multimapdotbothA L \strictiff \Colonsim \multimapdotbothAvert \succeqq \colonsim \multimapdotbothB \succneqq I \Eqcolon \multimapdotbothBvert ∥ \varparallel E \eqcolon \multimapdotbothvert \varparallelinv C \eqqcolon \multimapdotinv \VvDash G \Eqqcolon \multimapinv h \eqsim [ \openJoin

Table 46: txfonts/pxfonts Negated Binary Relations 6 \napproxeq $ \npreccurlyeq 5 \nthickapprox - \nasymp 9 \npreceqq h \ntwoheadleftarrow * \nbacksim \nprecsim g \ntwoheadrightarrow + \nbacksimeq ; \nsimeq \nvarparallel ( \nbumpeq 8 \nsuccapprox \nvarparallelinv ) \nBumpeq % \nsucccurlyeq 1 \nVdash . \nequiv : \nsucceqq 7 \nprecapprox \nsuccsim

Table 47: mathabx Binary Relations \between \divides \risingdotseq \botdoteq \dotseq Ç \succapprox \Bumpedeq \eqbumped ¥ \succcurlyeq \bumpedeq \eqcirc Í \succdot \circeq \eqcolon Á \succsim \coloneq \fallingdotseq 6 \therefore \corresponds Ï \ggcurly \topdoteq ¶ \curlyeqprec Î \llcurly ( \vDash · \curlyeqsucc Æ \precapprox , \Vdash ) \DashV ¤ \preccurlyeq ( \VDash ) \Dashv Ì \precdot , \Vvdash - \dashVv À \precsim

21 Table 48: mathabx Negated Binary Relations \napprox M \notperp * \nvDash \ncong ¢ \nprec * \nVDash ¸ \ncurlyeqprec È \nprecapprox . \nVdash ¹ \ncurlyeqsucc ¦ \npreccurlyeq & \nvdash + \nDashv ª \npreceq . \nVvash / \ndashV Â \nprecsim Ê \precnapprox ' \ndashv \nsim ¬ \precneq + \nDashV \nsimeq Ä \precnsim / \ndashVv £ \nsucc Ë \succnapprox \neq É \nsuccapprox \succneq \notasymp § \nsucccurlyeq Å \succnsim \notdivides « \nsucceq \notequiv Ã \nsuccsim

The \changenotsign command toggles the behavior of \not to produce either a vertical or a diagonal slash through a binary operator. Thus, “$a \not= b$” can be made to produce either “a = b” or “a = b”.

Table 49: Subset and Superset Relations ∗ @ \sqsubset w \sqsupseteq ⊃ \supset v \sqsubseteq ⊂ \subset ⊇ \supseteq ∗ A \sqsupset ⊆ \subseteq

∗ Not predeﬁned in LATEX 2ε. Use one of the packages latexsym, amsfonts, amssymb, mathabx, txfonts, pxfonts, or wasysym.

Table 50: AMS Subset and Superset Relations * \nsubseteq j \subseteqq % \supsetneqq + \nsupseteq ( \subsetneq \varsubsetneq # \nsupseteqq $ \subsetneqq & \varsubsetneqq @ \sqsubset c \Supset ! \varsupsetneq A \sqsupset k \supseteqq ' \varsupsetneqq b \Subset ) \supsetneq

Table 51: stmaryrd Subset and Superset Relations \subsetplus \supsetplus D \subsetpluseq E \supsetpluseq F G

Table 52: wasysym Subset and Superset Relations

@ \sqsubset A \sqsupset

22 Table 53: txfonts/pxfonts Subset and Superset Relations a \nsqsubset A \nsqsupseteq ? \nSupset @ \nsqsubseteq > \nSubset b \nsqsupset " \nsubseteqq

Table 54: mathabx Subset and Superset Relations \nsqsubset \nsupset \sqsupseteq \supseteq \nsqSubset \nSupset \sqsupseteqq \supseteqq \nsqsubseteq \nsupseteq \sqsupsetneq \supsetneq \nsqsubseteqq \nsupseteqq \sqsupsetneqq \supsetneqq \nsqsupset \sqsubset \subset \varsqsubsetneq \nsqSupset \sqSubset \Subset \varsqsubsetneqq \nsqsupseteq \sqsubseteq \subseteq \varsqsupsetneq \nsqsupseteqq \sqsubseteqq \subseteqq \varsqsupsetneqq \nsubset \sqsubsetneq \subsetneq \varsubsetneq \nSubset \sqsubsetneqq \subsetneqq \varsubsetneqq \nsubseteq \sqSupset \supset \varsupsetneq \nsubseteqq \sqsupset \Supset \varsupsetneqq

Table 55: Inequalities ≥ \geq \gg ≤ \leq \ll , \neq

Table 56: AMS Inequalities 1 \eqslantgtr ≷ \gtrless \lneq 0 \eqslantless & \gtrsim \lneqq = \geqq \gvertneqq \lnsim > \geqslant 5 \leqq \lvertneqq ≫ \ggg 6 \leqslant \ngeq \gnapprox / \lessapprox \ngeqq \gneq l \lessdot \ngeqslant \gneqq Q \lesseqgtr ≯ \ngtr \gnsim S \lesseqqgtr \nleq ' \gtrapprox ≶ \lessgtr \nleqq m \gtrdot . \lesssim \nleqslant R \gtreqless ≪ \lll ≮ \nless T \gtreqqless \lnapprox

Table 57: wasysym Inequalities \apprge \apprle ? >

23 Table 58: txfonts/pxfonts Inequalities 4 \ngg ! \ngtrsim \nlesssim # \ngtrapprox " \nlessapprox 3 \nll & \ngtrless ' \nlessgtr

Table 59: mathabx Inequalities · \eqslantgtr ½ \gtreqless À \lesssim £ \ngtr ¶ \eqslantless ¿ \gtreqqless ! \ll É \ngtrapprox ¥ \geq » \gtrless Î \lll Ã \ngtrsim ¯ \geqq Á \gtrsim Ê \lnapprox ¦ \nleq " \gg µ \gvertneqq ¬ \lneq ° \nleqq Ï \ggg ¤ \leq ² \lneqq ¢ \nless Ë \gnapprox ® \leqq Ä \lnsim È \nlessapprox \gneq Æ \lessapprox ´ \lvertneqq Â \nlesssim ³ \gneqq Ì \lessdot ¹ \neqslantgtr « \nvargeq Å \gnsim ¼ \lesseqgtr ¸ \neqslantless ª \nvarleq Ç \gtrapprox ¾ \lesseqqgtr § \ngeq © \vargeq Í \gtrdot º \lessgtr ± \ngeqq ¨ \varleq

mathabx deﬁnes \leqslant and \le as synonyms for \leq, \geqslant and \ge as synonyms for \geq, \nleqslant as a synonym for \nleq, and \ngeqslant as a synonym for \ngeq.

Table 60: AMS Triangle Relations

J \blacktriangleleft 5 \ntrianglelefteq E \trianglelefteq C \vartriangleleft I \blacktriangleright 7 \ntriangleright , \triangleq B \vartriangleright 6 \ntriangleleft 4 \ntrianglerighteq D \trianglerighteq

Table 61: stmaryrd Triangle Relations \trianglelefteqslant \trianglerighteqslant P \ntrianglelefteqslant Q \ntrianglerighteqslant R S

Table 62: mathabx Triangle Relations \ntriangleleft \ntrianglerighteq \triangleright \vartriangleright \ntrianglelefteq \triangleleft \trianglerighteq \ntriangleright \trianglelefteq \vartriangleleft

24 Table 63: Arrows ⇓ \Downarrow ←− \longleftarrow - \nwarrow ↓ \downarrow ⇐= \Longleftarrow ⇒ \Rightarrow ←- \hookleftarrow ←→ \longleftrightarrow → \rightarrow ,→ \hookrightarrow ⇐⇒ \Longleftrightarrow & \searrow { \leadsto∗ 7−→ \longmapsto . \swarrow ← \leftarrow =⇒ \Longrightarrow ↑ \uparrow ⇐ \Leftarrow −→ \longrightarrow ⇑ \Uparrow ⇔ \Leftrightarrow 7→ \mapsto l \updownarrow ↔ \leftrightarrow % \nearrow m \Updownarrow

∗ Not predeﬁned in LATEX 2ε. Use one of the packages latexsym, amsfonts, amssymb, txfonts, pxfonts, or wasysym.

Table 64: Harpoons ) \leftharpoondown + \rightharpoondown )* \rightleftharpoons ( \leftharpoonup * \rightharpoonup

Table 65: textcomp Text-Mode Arrows _ \textdownarrow \textrightarrow \textleftarrow ^ \textuparrow

Table 66: AMS Arrows \circlearrowleft ⇔ \leftleftarrows \rightleftarrows \circlearrowright \leftrightarrows ⇒ \rightrightarrows x \curvearrowleft ! \leftrightsquigarrow \rightsquigarrow y \curvearrowright W \Lleftarrow \Rsh c \dashleftarrow " \looparrowleft \twoheadleftarrow d \dashrightarrow # \looparrowright \twoheadrightarrow \downdownarrows \Lsh \upuparrows \leftarrowtail \rightarrowtail

Table 67: AMS Negated Arrows : \nLeftarrow < \nLeftrightarrow ; \nRightarrow 8 \nleftarrow = \nleftrightarrow 9 \nrightarrow

Table 68: AMS Harpoons \downharpoonleft \leftrightharpoons \upharpoonleft \downharpoonright \rightleftharpoons \upharpoonright

25 Table 69: stmaryrd Arrows \leftarrowtriangle ⇐ \Mapsfrom \shortleftarrow ^ \leftrightarroweq ←\ \mapsfrom \shortrightarrow - \leftrightarrowtriangle ⇒[ \Mapsto \shortuparrow ] \lightning \nnearrow \ssearrow ⇐ = \Longmapsfrom 1 \nnwarrow % \sswarrow ←−\ \longmapsfrom 0 \rightarrowtriangle $ =⇒[ \Longmapsto _ \shortdownarrow

Table 70: txfonts/pxfonts Arrows \boxdotLeft \circleddotright \Diamondleft \boxdotleft \circleleft \Diamondright \boxdotright \circleright \DiamondRight \boxdotRight e \dashleftrightarrow f \leftsquigarrow \boxLeft \DiamonddotLeft t \Nearrow \boxleft \Diamonddotleft v \Nwarrow \boxright \Diamonddotright V \Rrightarrow \boxRight \DiamonddotRight u \Searrow \circleddotleft \DiamondLeft w \Swarrow

Table 71: mathabx Arrows ö \circlearrowleft Ð \leftarrow Ô \nwarrow ÷ \circlearrowright Ð \leftleftarrows æ \restriction ó \curvearrowbotleft Ø \leftrightarrow Ñ \rightarrow õ \curvearrowbotleftright Ô \leftrightarrows Õ \rightleftarrows ô \curvearrowbotright ú \leftrightsquigarrow Ñ \rightrightarrows ð \curvearrowleft ø \leftsquigarrow ù \rightsquigarrow ò \curvearrowleftright ü \lefttorightarrow ý \righttoleftarrow ñ \curvearrowright î \looparrowdownleft é \Rsh ê \dlsh ï \looparrowdownright × \searrow Ó \downdownarrows ì \looparrowleft Ö \swarrow ÿ \downtouparrow í \looparrowright Ö \updownarrows × \downuparrows è \Lsh þ \uptodownarrow ë \drsh Õ \nearrow Ò \upuparrows

Table 72: mathabx Negated Arrows ö \nLeftarrow Ü \nleftrightarrow Û \nrightarrow Ú \nleftarrow ø \nLeftrightarrow ÷ \nRightarrow

26 Table 73: mathabx Harpoons Þ \barleftharpoon à \leftharpoonup é \rightleftharpoons ß \barrightharpoon Ø \leftleftharpoons Ù \rightrightharpoons Û \downdownharpoons à \leftrightharpoon ê \updownharpoons å \downharpoonleft è \leftrightharpoons ä \upharpoonleft ç \downharpoonright Ý \rightbarharpoon æ \upharpoonright ë \downupharpoons ã \rightharpoondown Ú \upupharpoons Ü \leftbarharpoon á \rightharpoonup â \leftharpoondown á \rightleftharpoon

Table 74: ulsy Contradiction Symbols © \blitza \blitzb \blitzc \blitzd \blitze

Table 75: Extension Characters − \relbar = \Relbar

Table 76: stmaryrd Extension Characters \Arrownot \Mapsfromchar \Mapstochar Y \arrownot \ \mapsfromchar X [

Table 77: txfonts/pxfonts Extension Characters \Mappedfromchar \Mmappedfromchar \Mmapstochar \mappedfromchar \mmappedfromchar \mmapstochar

Table 78: mathabx Extension Characters ß \mapsfromchar Þ \mapstochar û \Mapsfromchar ú \Mapstochar

Table 79: Log-like Symbols \arccos \cos \csc \exp \ker \limsup \min \sinh \arcsin \cosh \deg \gcd \lg \ln \Pr \sup \arctan \cot \det \hom \lim \log \sec \tan \arg \coth \dim \inf \liminf \max \sin \tanh

Calling the above “symbols” may be a bit misleading.1 Each log-like symbol merely produces the eponymous textual equivalent, but with proper surrounding spacing. See Section 7.3 for more information about log-like symbols. As \bmod and \pmod are arguably not symbols we refer the reader to the Short Math Guide for LATEX [Dow00] for samples.

27 Table 80: AMS Log-like Symbols

inj lim lim lim \injlim −→ \varinjlim \varlimsup proj lim lim lim \projlim \varliminf ←− \varprojlim

Load the amsmath package to get these symbols. See Section 7.3 for some additional comments regarding log-like symbols. As \mod and \pod are arguably not symbols we refer the reader to the Short Math Guide for LATEX [Dow00] for samples.

Table 81: Greek Letters α \alpha θ \theta o o τ \tau β \beta ϑ \vartheta π \pi υ \upsilon γ \gamma ι \iota $ \varpi φ \phi δ \delta κ \kappa ρ \rho ϕ \varphi \epsilon λ \lambda % \varrho χ \chi ε \varepsilon µ \mu σ \sigma ψ \psi ζ \zeta ν \nu ς \varsigma ω \omega η \eta ξ \xi

Γ \Gamma Λ \Lambda Σ \Sigma Ψ \Psi ∆ \Delta Ξ \Xi Υ \Upsilon Ω \Omega Θ \Theta Π \Pi Φ \Phi

The remaining Greek majuscules can be produced with ordinary Latin letters. The symbol “M”, for instance, is used for both an uppercase “m” and an uppercase “µ”.

Table 82: AMS Greek Letters z \digamma κ \varkappa

Table 83: txfonts/pxfonts Upright Greek Letters α \alphaup θ \thetaup π \piup φ \phiup β \betaup ϑ \varthetaup $ \varpiup ϕ \varphiup γ \gammaup ι \iotaup ρ \rhoup χ \chiup δ \deltaup κ \kappaup % \varrhoup ψ \psiup \epsilonup λ \lambdaup σ \sigmaup ω \omegaup ε \varepsilonup µ \muup ς \varsigmaup ζ \zetaup ν \nuup τ \tauup η \etaup ξ \xiup υ \upsilonup

Table 84: txfonts/pxfonts Variant Latin Letters 1 \varg 3 \varv 4 \varw 2 \vary

Pass the varg option to txfonts/pxfonts to replace g, v, w, and y with 1, 3, 4, and 2 in every mathematical expression in your document.

1Michael J. Downes prefers the more general term, “atomic math objects”.

28 Table 85: AMS Hebrew Letters gimel k \daleth\ ג i \beth

\aleph appears in Table 109 on page 33.

Table 86: Letter-like Symbols ⊥ \bot ∀ \forall ı \imath 3 \ni > \top ` \ell ~ \hbar ∈ \in ∂ \partial ℘ \wp ∃ \exists = \Im  \jmath < \Re

Table 87: AMS Letter-like Symbols k \Bbbk { \complement ~ \hbar r \circledR ` \Finv } \hslash s \circledS a \Game @ \nexists

Table 88: txfonts/pxfonts Letter-like Symbols ¢ \mathcent £ \mathsterling < \notin = \notni

Table 89: mathabx Letter-like Symbols V \barin P \in L \nottop T \varnotin A \complement E \nexists Q \owns U \varnotowner D \exists M \notbot W \ownsbar F \Finv R \notin B \partial G \Game S \notowner C \partialslash

Table 90: AMS Delimiters p \ulcorner q \urcorner x \llcorner y \lrcorner

Table 91: stmaryrd Delimiters P \Lbag Q \Rbag N \lbag O \rbag \llceil \rrceil \llfloor \rrfloor V \llparenthesis W \rrparenthesis T U L M

Table 92: mathabx Delimiters v \lcorners w \rcorners

x \ulcorner y \urcorner z \llcorner { \lrcorner

29 Table 93: Variable-sized Delimiters ? w h i ? w ↓ y \downarrow ⇓ \Downarrow [ [ ] ] D E h \langle i \rangle | |∗ k \| l m x ~ ? w d \lceil e \rceil ↑ ? \uparrow ⇑ w \Uparrow j k x ~ ? w b \lfloor c \rfloor l y \updownarrow m \Updownarrow n o ( ( ) ) { \{ } \} . / / / \ \backslash

When used with \left and \right, these symbols expand to the height of the enclosed math expression. Note that \vert is a synonym for |, and \Vert is a synonym for \|.

∗ e-TEX provides a \middle analogue to \left and \right that can be used to make an internal “|” expand to the height of the surrounding \left and \right symbols. A similar eﬀect can be achieved in conventional LATEX using the braket package.

Table 94: Large, Variable-Sized Delimiters 8 9 8 9 8 > 9 > 8 > 9 > ; > : > : > ; > ;> \lmoustache :> \rmoustache :> \lgroup ;> \rgroup ? w > ? ? w w > > ? ? w w > > ? \arrowvert w \Arrowvert > > \bracevert ? w >

These symbols must be used with \left and \right. The mathabx package, however, redeﬁnes \lgroup and \rgroup so that those symbols can work without \left and \right.

Table 95: Variable-Sized stmaryrd Delimiters

~ \llbracket \rrbracket

Table 96: mathabx Variable-Sized Delimiters 1 9 v \lbbbrack w \rbbbrack 7 ? 7 ? 7 ? 7 7 \lfilet ? ? \rfilet ~ \thickvert ~ \vvvert

30 Table 97: textcomp Text-Mode Delimiters < \textlangle > \textrangle [ \textlbrackdbl ] \textrbrackdbl \textlquill ¡ \textrquill

Table 98: Math-Mode Accents a´ \acute{a} aˇ \check{a} a` \grave{a} a˜ \tilde{a} a¯ \bar{a} a¨ \ddot{a} aˆ \hat{a} ~a \vec{a} a˘ \breve{a} a˙ \dot{a} ˚a \mathring{a}

Also note the existence of \imath and \jmath, which produce dotless versions of “i” and “j ”. (See Table 109 on page 33.) These are useful when the accent is supposed to replace the dot. For example, “\hat{\imath}” produces a correct “ˆı ”, while “\hat{i}” would yield the rather odd-looking “ˆi ”.

Table 99: AMS Math-Mode Accents ...... a \dddot{a} a \ddddot{a}

These accents are also provided by the mathabx package.

Table 100: yhmath Math-Mode Accents ˚a \ring{a}

This symbol is largely obsolete, as standard LATEX 2ε has supported \mathring since June, 1998 [LAT98].

Table 101: Extensible Accents abcÝ \widetilde{abc}∗ abcÓ \widehat{abc}∗ ←− −→ abc \overleftarrow{abc} abc \overrightarrow{abc} abc \overline{abc} abc \underline{abc} z}|{ abc \overbrace{abc} |{z}abc \underbrace{abc} √ √ abc \sqrt{abc} n abc \sqrt[n]{abc}

∗ Made more extensible by the yhmath package.

Table 102: yhmath Extensible Accents

abcö \wideparen{abc} abcé \widetriangle{abc} ˚ abcö \widering{abc}

31 Table 103: AMS Extensible Accents ←→ abc \overleftrightarrow{abc} ←→abc \underleftrightarrow{abc} ←−abc \underleftarrow{abc} −→abc \underrightarrow{abc}

The following are a sort of “reverse accent” in that the argument text serves as a superscript to the arrow. In addition, the optional ﬁrst argument (not shown) serves as a subscript to the arrow. See the Short Math Guide for LATEX [Dow00] for further examples.

abc abc ←−− \xleftarrow{abc} −−→ \xrightarrow{abc}

Table 104: mathabx Extensible Accents hkkikkj abc \overbrace{abc} abc \widebar{abc} hkkkkj abc \overgroup{abc} abc| \widecheck{abc}

loomoonabc \underbrace{abc} abc \wideparen{abc} ˚ loooonabc \undergroup{abc} abcö \widering{abc}

abc \widearrow{abc}

The braces shown for \overbrace and \underbrace appear in their minimum size. They can expand arbitrarily wide, however.

Table 105: esvect Extensible Accents # ” abc \vv{abc} with package option a # „ abc \vv{abc} with package option b # « abc \vv{abc} with package option c # » abc \vv{abc} with package option d # – abc \vv{abc} with package option e # — abc \vv{abc} with package option f # abc \vv{abc} with package option g # ‰ abc \vv{abc} with package option h esvect also deﬁnes a \vv* macro which is used to typeset arrows over vector vari- ables with subscripts. See the esvect documentation for more information.

32 Table 106: Dots . · \cdotp : \colon∗ . \ldotp . \vdots . ··· \cdots .. \ddots ... \ldots

∗ While “:” is valid in math mode, \colon uses diﬀerent surrounding spacing. See Section 7.3 and the Short Math Guide for LATEX [Dow00] for more information on math-mode spacing.

Table 107: AMS Dots ··· \dotsb ··· \dotsi ... \dotso ... \dotsc ··· \dotsm

The AMS dot symbols are named according to their intended usage: \dotsb between pairs of binary operators/relations, \dotsc between pairs of commas, \dotsi between pairs of integrals, \dotsm between pairs of multiplication signs, and \dotso between other symbol pairs.

Table 108: yhmath Dots . .. \adots

Table 109: Miscellaneous LATEX 2ε Symbols ℵ \aleph ^ \Diamond∗ ∞ \infty 0 \prime 6 \angle ♦ \diamondsuit f \mho∗ ] \sharp \ \backslash ∅ \emptyset ∇ \nabla ♠ \spadesuit ∗ √ \Box [ \flat \ \natural \surd ♣ \clubsuit ♥ \heartsuit ¬ \neg 4 \triangle

∗ Not predeﬁned in LATEX 2ε. Use one of the packages latexsym, amsfonts, amssymb, txfonts, pxfonts, or wasysym.

Table 110: Miscellaneous AMS Symbols ∠ \angle H \blacktriangledown f \mho 8 \backprime \diagdown ^ \sphericalangle F \bigstar \diagup \square \blacklozenge ð \eth O \triangledown \blacksquare ♦ \lozenge ∅ \varnothing N \blacktriangle ] \measuredangle M \vartriangle

33 Table 111: Miscellaneous wasysym Symbols ∗ \Box f \mho \wasytherefore ^ \Diamond \varangle ∴ ∗ wasysym also deﬁnes an \agemO symbol, which is the same glyph as \mho but is intended for use in text mode.

Table 112: Miscellaneous txfonts/pxfonts Symbols _ \Diamondblack n \lambdaslash r \varheartsuit \Diamonddot p \varclubsuit s \varspadesuit o \lambdabar q \vardiamondsuit

Table 113: Miscellaneous mathabx Symbols 0 \degree 4 \fourth > \measuredangle 2 \second å \diagdown # \hash & \pitchfork ? \sphericalangle ä \diagup 8 \infty 9 \propto 3 \third I \diameter $ \leftthreetimes % \rightthreetimes # \varhash

Table 114: Miscellaneous textcomp Text-Mode Math Symbols ° \textdegree ½ \textonehalf ¾ \textthreequarters ö \textdiv ¼ \textonequarter ³ \textthreesuperior / \textfractionsolidus ¹ \textonesuperior Ö \texttimes ¬ \textlnot ± \textpm ² \texttwosuperior = \textminus » \textsurd

Table 115: mathcomp Math Symbols \tccentigrade W \tcohm \tcperthousand µ \tcmu \tcpertenthousand

Table 116: mathabx Mayan Digits 0 \maya{0} 2 \maya{2} 4 \maya{4} 1 \maya{1} 3 \maya{3} 5 \maya{5}

Table 117: marvosym Math Symbols 0 \MVZero 2 \MVTwo 4 \MVFour 6 \MVSix 8 \MVEight 1 \MVOne 3 \MVThree 5 \MVFive 7 \MVSeven 9 \MVNine

W \Anglesign ÷ \Squaredot P \Vectorarrowhigh = \Corresponds p \Vectorarrow

34 Table 118: Math Alphabets Required package ABCdef123 \mathrm{ABCdef123} none ABCdef123 \mathit{ABCdef123} none ABCdef \mathnormal{ABCdef123} none ABC \mathcal{ABC} none ABC \mathscr{ABC} mathrsfs ABC \mathcal{ABC} euscript with the mathcal option or \mathscr{ABC} euscript with the mathscr option ABCdef123 \mathpzc{ABCdef123} none; manually deﬁned∗ ABC \mathbb{ABC} amsfonts, amssymb, txfonts, or pxfonts º»¼ \varmathbb{ABC} txfonts or pxfonts ABCdef123 \mathbb{ABCdef123} bbold or mathbbol† ABCdef12 \mathbbm{ABCdef12} bbm ABCdef12 \mathbbmss{ABCdef12} bbm ABCdef12 \mathbbmtt{ABCdef12} bbm ABC1 \mathds{ABC1} dsfont ABC1 \mathds{ABC1} dsfont with the sans option ABCdef123 \mathfrak{ABCdef123} eufrak ABCdef123 \textfrak{ABCdef123} yfonts ABCdef123 \textswab{ABCdef123} yfonts

∗ Put “\DeclareMathAlphabet{\mathpzc}{OT1}{pzc}{m}{it}” in your document’s preamble to make \mathpzc typeset its argument in Zapf Chancery.

† The mathbbol package deﬁnes some additional blackboard bold characters: parentheses, square brackets, angle brackets, and—if the bbgreekl option is passed to matbbol—Greek letters. For instance, “<[( )]>” is produced by “\mathbb{\Langle\Lbrack\Lparen\bbalpha\bbbeta\bbgamma\Rparen \Rbrack\Rangle}”.

35 4 Science and technology symbols

This section lists symbols that are employed in various branches of science and engineering (and, because we were extremely liberal in our classiﬁcation, astrology, too).

Table 119: wasysym Electrical and Physical Symbols \AC \VHF \photon \HF \gluon ¬ @ ¬¬¬¬ ¬ QPPPPPPR

Table 120: ifsym Pulse Diagram Symbols ! \FallingEdge ' \LongPulseLow % \PulseLow " \ShortPulseHigh & \LongPulseHigh $ \PulseHigh \RaisingEdge # \ShortPulseLow

In addition, within \textifsym{...}, the following codes are valid:

l l m m h h d d < < > > L L M M H H D D = << ? >>

This enables one to write “\textifsym{mmmm}” to get “mmmm” or “\textifsym{L|H|L|H|L}” to get “L|H|L|H|L”.

Finally, \textifsym supports the display of segmented digits, as would appear on an LCD: “\textifsym{-123.456}” produces “-123.456”. “\textifsym{b}” outputs a blank with the same width as an “8”.

Table 121: ar Aspect Ratio Symbol A \AR

Table 122: textcomp Text-Mode Science and Engineering Symbols \textcelsius M \textmho µ \textmu W \textohm

Table 123: wasysym Astronomical Symbols \ascnode \jupiter \newmoon \venus \astrosun X \leftmoon \pluto ♀ \vernal \descnode $ \mars \ \rightmoon \earth ♂ \mercury % \saturn ♁ \fullmoon ' \neptune Y \uranus # [ Z

Table 124: marvosym Astronomical Symbols Â \Mercury Ä \Mars Ç \Uranus À \Sun Ã \Venus Å \Jupiter È \Neptune Á \Moon Ê \Earth Æ \Saturn É \Pluto

36 Table 125: mathabx Astronomical Symbols A \Mercury C \Earth E \Jupiter G \Uranus I \Pluto B \Venus D \Mars F \Saturn H \Neptune

M \fullmoon K \leftmoon N \newmoon L \rightmoon @ \Sun J \varEarth

mathabx also deﬁnes \girl as an alias for \Venus, \boy as an alias for \Mars, and \Moon as an alias for \leftmoon.

Table 126: wasysym Astrological Symbols \aries \cancer \libra \capricornus \taurus _ \leo a \scorpio d \aquarius ] \gemini \virgo b \sagittarius e \pisces ^ ` c f \conjunction \opposition V W

Table 127: marvosym Astrological Symbols à \Aries ã \Cancer æ \Libra é \Capricorn á \Taurus ä \Leo ç \Scorpio ê \Aquarius â \Gemini å \Virgo è \Sagittarius ë \Pisces

Note that \Aries ... \Pisces can also be speciﬁed with \Zodiac{1} ... \Zodiac{12}.

Table 128: mathabx Astrological Symbols P \Aries Q \Taurus R \Gemini

Table 129: wasysym APL Symbols \APLbox ÷ \APLinv \APLstar ~ \APLcomment ~ \APLleftarrowbox E \APLup \APLdown p \APLlog \APLuparrowbox − F \APLdownarrowbox \APLminus n\− \notbackslash o \APLinput \APLrightarrowbox −/ \notslash } q

Table 130: wasysym APL Modiﬁers ◦ \APLcirc{} ∼ \APLnot{} | \APLvert{}

Table 131: marvosym Computer Hardware Symbols Í \ComputerMouse Ñ \ParallelPort Î \SerialInterface Ï \Keyboard Ò \Printer Ð \SerialPort

37 Table 132: ascii Control Characters (IBM) \SOH • \BEL ♪ \CR ‼ \DCc ↓ \EM \US \STX \BS ♫ \SO ¶ \DCd → \SUB ¦ \splitvert ♥ \ETX \HT \SI § \NAK ← \ESC \DEL ♦ \EOT \LF \DLE \SYN └ \FS ♣ \ENQ ♂ \VT \DCa \ETB ↔ \GS ♠ \ACK ♀ \FF \DCb ↑ \CAN \RS

SOH, STX, ETX, ..., US are the names of ASCII characters 1–31. DEL is the name of ASCII character 127. \splitvert doesn’t correspond to a control character but is merely the “|” character shown IBM style.

These characters must be entered with the ascii font in eﬀect, for example, “{\ascii\STX}”. See the ascii package documentation for more information.

Table 133: marvosym Communication Symbols k \Email t \fax v \Faxmachine E \Lightning A \Pickup z \Emailct u \FAX B \Letter H \Mobilefone T \Telefon

Table 134: marvosym Engineering Symbols " \Beam l \Force ‘ \Octosteel \RoundedTTsteel # \Bearing ’ \Hexasteel ˜ \Rectpipe — \Squarepipe › \Circpipe & \Lefttorque ” \Rectsteel “ \Squaresteel • \Circsteel L \Lineload ' \Righttorque œ \Tsteel ∗ % \Fixedbearing $ \Loosebearing Ÿ \RoundedLsteel š \TTsteel ∗ – \Flatsteel ™ \Lsteel \RoundedTsteel

∗ \RoundedLsteel and \RoundedTsteel seem to be swapped, at least in the 2000/05/01 version of marvosym.

Table 135: wasysym Biological Symbols \female \male ♀ ♂

Table 136: marvosym Biological Symbols ~ \Female … \FemaleMale ‚ \MALE { \Neutral \FEMALE } \Hermaphrodite | \Male „ \FemaleFemale \HERMAPHRODITE ƒ \MaleMale

Table 137: marvosym Safety-Related Symbols h \Biohazard C \CEsign ` \Explosionsafe j \Radioactivity n \BSEfree J \Estatically a \Laserbeam ! \Stopsign

38 5 Dingbats

Dingbats are symbols such as stars, arrows, and geometric shapes. They are commonly used as bullets in itemized lists or, more generally, as a means to draw attention to the text that follows. The pifont dingbat package warrants special mention. Among other capabilities, pifont provides a LATEX interface to the Zapf Dingbats font (one of the standard 35 PostScript fonts). However, rather than name each of the dingbats individually, pifont merely provides a single \ding command, which outputs the character that lies at a given position in the font. The consequence is that the pifont symbols can’t be listed by name in this document’s index, so be mindful of that fact when searching for a particular symbol.

Table 138: bbding Arrows y \ArrowBoldDownRight z \ArrowBoldRightShort x \ArrowBoldUpRight { \ArrowBoldRightCircled w \ArrowBoldRightStrobe

Table 139: pifont Arrows ➔ \ding{212} ➝ \ding{221} ➦ \ding{230} ➯ \ding{239} ➹ \ding{249} → \ding{213} ➞ \ding{222} ➧ \ding{231} ➱ \ding{241} ➺ \ding{250} ↔ \ding{214} ➟ \ding{223} ➨ \ding{232} ➲ \ding{242} ➻ \ding{251} ↕ \ding{215} ➠ \ding{224} ➩ \ding{233} ➳ \ding{243} ➼ \ding{252} ➘ \ding{216} ➡ \ding{225} ➪ \ding{234} ➴ \ding{244} ➽ \ding{253} ➙ \ding{217} ➢ \ding{226} ➫ \ding{235} ➵ \ding{245} ➾ \ding{254} ➚ \ding{218} ➣ \ding{227} ➬ \ding{236} ➶ \ding{246} ➛ \ding{219} ➤ \ding{228} ➭ \ding{237} ➷ \ding{247} ➜ \ding{220} ➥ \ding{229} ➮ \ding{238} ➸ \ding{248}

Table 140: marvosym Scissors s \Cutleft q \Cutright S \Leftscissors r \Cutline R \Kutline Q \Rightscissors

Table 141: bbding Scissors § \ScissorHollowLeft ¥ \ScissorLeftBrokenTop ¦ \ScissorHollowRight ¡ \ScissorRight ¤ \ScissorLeft \ScissorRightBrokenBottom £ \ScissorLeftBrokenBottom ¢ \ScissorRightBrokenTop

Table 142: pifont Scissors ✁ \ding{33} ✂ \ding{34} ✃ \ding{35} ✄ \ding{36}

Table 143: dingbat Pencils

W \largepencil P \smallpencil

39 Table 144: bbding Pencils and Nibs \NibLeft \PencilLeft \PencilRightDown \NibRight \PencilLeftDown \PencilRightUp \NibSolidLeft \PencilLeftUp \NibSolidRight \PencilRight

Table 145: pifont Pencils and Nibs ✎ \ding{46} ✏ \ding{47} ✐ \ding{48} ✑ \ding{49} ✒ \ding{50}

Table 146: dingbat Hands

R \leftpointright L \rightpointleft N \rightpointright D \leftthumbsdown d \rightthumbsdown U \leftthumbsup u \rightthumbsup

Table 147: bbding Hands \HandCuffLeft \HandCuffRightUp \HandPencilLeft \HandCuffLeftUp \HandLeft \HandRight \HandCuffRight \HandLeftUp \HandRightUp

Table 148: pifont Hands ☛ \ding{42} ☞ \ding{43} ✌ \ding{44} ✍ \ding{45}

Table 149: bbding Crosses and Plusses * \Cross + \CrossOpenShadow & \PlusOutline - \CrossBoldOutline , \CrossOutline ) \PlusThinCenterOpen 4 \CrossClowerTips ' \Plus . \CrossMaltese ( \PlusCenterOpen

Table 150: pifont Crosses and Plusses ✙ \ding{57} ✛ \ding{59} ✝ \ding{61} ✟ \ding{63} ✚ \ding{58} ✜ \ding{60} ✞ \ding{62} ✠ \ding{64}

Table 151: bbding Xs and Check Marks ! \Checkmark # \XSolid % \XSolidBrush " \CheckmarkBold $ \XSolidBold

40 Table 152: pifont Xs and Check Marks ✓ \ding{51} ✕ \ding{53} ✗ \ding{55} ✔ \ding{52} ✖ \ding{54} ✘ \ding{56}

Table 153: wasysym Xs and Check Marks

\CheckedBox \Square \XBox 2 4

Table 154: pifont Circled Numbers ① \ding{172} ❶ \ding{182} ➀ \ding{192} ➊ \ding{202} ② \ding{173} ❷ \ding{183} ➁ \ding{193} ➋ \ding{203} ③ \ding{174} ❸ \ding{184} ➂ \ding{194} ➌ \ding{204} ④ \ding{175} ❹ \ding{185} ➃ \ding{195} ➍ \ding{205} ⑤ \ding{176} ❺ \ding{186} ➄ \ding{196} ➎ \ding{206} ⑥ \ding{177} ❻ \ding{187} ➅ \ding{197} ➏ \ding{207} ⑦ \ding{178} ❼ \ding{188} ➆ \ding{198} ➐ \ding{208} ⑧ \ding{179} ❽ \ding{189} ➇ \ding{199} ➑ \ding{209} ⑨ \ding{180} ❾ \ding{190} ➈ \ding{200} ➒ \ding{210} ⑩ \ding{181} ❿ \ding{191} ➉ \ding{201} ➓ \ding{211}

pifont (part of the psnfss package) provides a dingautolist environment which resembles enumerate but uses circled numbers as bullets.2 See the psnfss documentation for more information.

Table 155: wasysym Stars \davidsstar \hexstar \varhexstar C A B

Table 156: bbding Stars, Flowers, and Similar Shapes N \Asterisk P \FiveFlowerPetal 2 \JackStar A \AsteriskBold 8 \FiveStar 3 \JackStarBold B \AsteriskCenterOpen ; \FiveStarCenterOpen O \SixFlowerAlternate X \AsteriskRoundedEnds ? \FiveStarConvex U \SixFlowerAltPetal C \AsteriskThin 7 \FiveStarLines M \SixFlowerOpenCenter D \AsteriskThinCenterOpen 9 \FiveStarOpen Q \SixFlowerPetalDotted 0 \DavidStar : \FiveStarOpenCircled L \SixFlowerPetalRemoved / \DavidStarSolid < \FiveStarOpenDotted [ \SixFlowerRemovedOpenPetal Z \EightAsterisk = \FiveStarOutline G \SixStar S \EightFlowerPetal > \FiveStarOutlineHeavy K \SixteenStarLight Y \EightFlowerPetalRemoved @ \FiveStarShadow ` \Snowflake H \EightStar 1 \FourAsterisk ^ \SnowflakeChevron I \EightStarBold V \FourClowerOpen _ \SnowflakeChevronBold F \EightStarConvex W \FourClowerSolid ] \Sparkle E \EightStarTaper 5 \FourStar \ \SparkleBold R \FiveFlowerOpen 6 \FourStarOpen J \TwelweStar

2In fact, dingautolist can use any set of consecutive Zapf Dingbats symbols.

41 Table 157: pifont Stars, Flowers, and Similar Shapes ✡ \ding{65} ✪ \ding{74} ✳ \ding{83} ✼ \ding{92} ❅ \ding{101} ✢ \ding{66} ✫ \ding{75} ✴ \ding{84} ✽ \ding{93} ❆ \ding{102} ✣ \ding{67} ✬ \ding{76} ✵ \ding{85} ✾ \ding{94} ❇ \ding{103} ✤ \ding{68} ✭ \ding{77} ✶ \ding{86} ✿ \ding{95} ❈ \ding{104} ✥ \ding{69} ✮ \ding{78} ✷ \ding{87} ❀ \ding{96} ❉ \ding{105} ✦ \ding{70} ✯ \ding{79} ✸ \ding{88} ❁ \ding{97} ❊ \ding{106} ✧ \ding{71} ✰ \ding{80} ✹ \ding{89} ❂ \ding{98} ❋ \ding{107} ★ \ding{72} ✱ \ding{81} ✺ \ding{90} ❃ \ding{99} ✩ \ding{73} ✲ \ding{82} ✻ \ding{91} ❄ \ding{100}

Table 158: wasysym Geometric Shapes \hexagon \octagon \pentagon \varhexagon 7 8 D 9

Table 159: ifsym Geometric Shapes % \BigCircle T \FilledBigTriangleRight E \SmallCircle \BigCross Q \FilledBigTriangleUp \SmallCross & \BigDiamondshape e \FilledCircle F \SmallDiamondshape \BigHBar ¨ \FilledDiamondShadowA \SmallHBar _ \BigLowerDiamond © \FilledDiamondShadowC \SmallLowerDiamond / \BigRightDiamond f \FilledDiamondshape O \SmallRightDiamond \BigSquare u \FilledSmallCircle @ \SmallSquare # \BigTriangleDown v \FilledSmallDiamondshape C \SmallTriangleDown " \BigTriangleLeft p \FilledSmallSquare B \SmallTriangleLeft $ \BigTriangleRight s \FilledSmallTriangleDown D \SmallTriangleRight ! \BigTriangleUp r \FilledSmallTriangleLeft A \SmallTriangleUp \BigVBar t \FilledSmallTriangleRight \SmallVBar 5 \Circle q \FilledSmallTriangleUp * \SpinDown \Cross ` \FilledSquare ) \SpinUp ¥ \DiamondShadowA £ \FilledSquareShadowA 0 \Square ¦ \DiamondShadowB ¤ \FilledSquareShadowC \SquareShadowA § \DiamondShadowC c \FilledTriangleDown ¡ \SquareShadowB 6 \Diamondshape b \FilledTriangleLeft ¢ \SquareShadowC U \FilledBigCircle d \FilledTriangleRight 3 \TriangleDown V \FilledBigDiamondshape a \FilledTriangleUp 2 \TriangleLeft P \FilledBigSquare \HBar 4 \TriangleRight S \FilledBigTriangleDown o \LowerDiamond 1 \TriangleUp R \FilledBigTriangleLeft ? \RightDiamond \VBar

The ifsym documentation points out that one can use \rlap to combine some of the above into useful, new symbols. For example, \BigCircle and \FilledSmallCircle combine to give “ u% ”. Likewise, \Square and \Cross combine to give “0”. See Section 7.2 for more information about constructing new symbols out of existing symbols.

42 Table 160: bbding Geometric Shapes d \CircleShadow u \Rectangle j \SquareShadowTopLeft a \CircleSolid v \RectangleBold i \SquareShadowTopRight p \DiamondSolid t \RectangleThin g \SquareSolid b \Ellipse f \Square o \TriangleDown e \EllipseShadow k \SquareCastShadowBottomRight n \TriangleUp c \EllipseSolid m \SquareCastShadowTopLeft s \HalfCircleLeft l \SquareCastShadowTopRight r \HalfCircleRight h \SquareShadowBottomRight

Table 161: pifont Geometric Shapes ● \ding{108} ❏ \ding{111} ❒ \ding{114} ◆ \ding{117} ❙ \ding{121} ❍ \ding{109} ❐ \ding{112} ▲ \ding{115} ◗ \ding{119} ❚ \ding{122} ■ \ding{110} ❑ \ding{113} ▼ \ding{116} ❘ \ding{120}

Table 162: manfnt Dangerous Bend Symbols \dbend ~ \lhdbend \reversedvideodbend

Note that these symbols descend far beneath the baseline. manfnt also deﬁnes non- descending versions, which it calls, correspondingly, \textdbend, \textlhdbend, and \textreversedvideodbend.

Table 163: skull Symbols A \skull

Table 164: Non-Mathematical mathabx Symbols O \rip

Table 165: marvosym Information Symbols ® \Bicycle o \Football Z \Pointinghand V \Checkedbox x \Gentsroom w \Wheelchair U \Clocklogo I \Industry b \Writinghand K \Coffeecup i \Info X \Crossedbox y \Ladiesroom

Table 166: Miscellaneous dingbat Dingbats

O \anchor E \eye S \Sborder C \carriagereturn C \filledsquarewithdots B \squarewithdots D \checkmark I \satellitedish Z \Zborder

43 Table 167: Miscellaneous bbding Dingbats \Envelope \Peace © \PhoneHandset T \SunshineOpenCircled q \OrnamentDiamondSolid ¨ \Phone \Plane \Tape

Table 168: Miscellaneous pifont Dingbats ☎ \ding{37} ✈ \ding{40} ❤ \ding{164} ❧ \ding{167} ♠ \ding{171} ✆ \ding{38} ✉ \ding{41} ❥ \ding{165} ♣ \ding{168} ♦ \ding{169} ✇ \ding{39} ❖ \ding{118} ❦ \ding{166} ♥ \ding{170}

44 6 Other symbols

The following are all the symbols that didn’t ﬁt neatly or unambiguously into any of the previous sections. (Do weather symbols belong under “Science and technology”? Should dice be considered “mathematics”?) While some of the tables contain clearly related groups of symbols (e.g., musical notes), others represent motley assortments of whatever the font designer felt like drawing.

Table 169: textcomp Genealogical Symbols b \textborn c \textdivorced m \textmarried d \textdied l \textleaf

Table 170: wasysym General Symbols \ataribox \clock \LEFTarrow \smiley m \bell \diameter \lightning , \sun \blacksmiley \DOWNarrow \phone ☼ \UParrow - \Bowtie L \frownie \pointer K \wasylozenge 1 \brokenvert / \invdiameter \recorder ◊ | \checked \kreuz \RIGHTarrow 6

Table 171: wasysym Musical Notes \eighthnote \halfnote \twonotes \fullnote \quarternote ♩ See also \flat, \sharp, and \natural (Table 109 on page 33).

Table 172: wasysym Circles \CIRCLE \LEFTcircle \RIGHTcircle \rightturn \Circle G# \Leftcircle H# \Rightcircle ! # \LEFTCIRCLE I \RIGHTCIRCLE J \leftturn G H "

Table 173: Miscellaneous manfnt Symbols \manboldkidney \manpenkidney $ \manconcentriccircles & \manquadrifolium % \manconcentricdiamond \manquartercircle # \mancone ' \manrotatedquadrifolium \mancube " \manrotatedquartercircle y \manerrarrow \manstar ! \manfilledquartercircle \mantiltpennib \manhpennib 7 \mantriangledown \manimpossiblecube x \mantriangleright \mankidney 6 \mantriangleup \manlhpenkidney \manvpennib

45 Table 174: marvosym Navigation Symbols · \Forward » \MoveDown ´ \RewindToIndex ¼ \ToTop ¸ \ForwardToEnd º \MoveUp µ \RewindToStart ¹ \ForwardToIndex ¶ \Rewind ½ \ToBottom

Table 175: marvosym Laundry Symbols Ø \AtForty Ü \Handwash Ô \ShortNinetyFive Ó \AtNinetyFive ¯ \IroningI Ö \ShortSixty Õ \AtSixty ° \IroningII Û \ShortThirty Ë \Bleech ± \IroningIII Ú \SpecialForty « \CleaningA Ì \NoBleech \Tumbler ¾ \CleaningF ¨ \NoChemicalCleaning ‰ \WashCotton ¿ \CleaningFF ² \NoIroning Š \WashSynthetics ¬ \CleaningP \NoTumbler ‹ \WashWool \CleaningPP × \ShortFifty Ý \Dontwash Ù \ShortForty

Table 176: Other marvosym Symbols ˆ \Ankh † \Cross Œ \Heart © \Smiley ý \Bat F \FHBOlogo ÿ \MartinVogel þ \Womanface ¥ \Bouquet f \FHBOLOGO m \Mundus Y \Yinyang ‡ \Celtcross § \Frowny @ \MVAt ∗ ª \CircledA \FullFHBO : \Rightarrow

∗ Standard LATEX 2ε defines \Rightarrow to display “⇒”, while marvosym redefines it to display “:” (or “:” in math mode). This conflict can be problematic for math symbols defined in terms of \Rightarrow, such as \Longleftrightarrow, which ends up looking like “⇐ :”.

Table 177: ifsym Weather Symbols \Cloud \Hail \Sleet \WeakRain \FilledCloud \HalfSun \Snow \WeakRainCloud ! \FilledRainCloud \Lightning \SnowCloud $ \FilledSnowCloud # \FilledSunCloud \NoSun \Sun " \FilledWeakRainCloud \Rain \SunCloud \Fog \RainCloud \ThinFog

Similarly, \wind{hsuni}{hanglei}{hstrengthi} will draw wind symbols with a given amount of sun (0–4), a given angle (in degrees), and a given strength in km/h (0– 100). For example, \wind{0}{0}{0} produces “ 0 ”, \wind{2}{0}{0} produces “¢ 0 ”, and \wind{4}{0}{100} produces “¤ : ”.

46 Table 178: ifsym Alpine Symbols \SummitSign \Summit \SurveySign \HalfFilledHut \StoneMan \Mountain \Joch \VarSummit \Hut \IceMountain \Flag \FilledHut \VarMountain \VarFlag \Village \VarIceMountain \Tent

Table 179: ifsym Clocks

\Interval \StopWatchStart \VarClock \Wecker \StopWatchEnd \Taschenuhr \VarTaschenuhr

ifsym also exports a \showclock macro. \showclock{hhoursi}{hminutesi} outputs a clock displaying the corresponding time. For instance, “\showclock{5}{40}” produces “D”. hhoursi must be an integer from 0 to 11, and hminutesi must be an integer multiple of 5 from 0 to 55.

Table 180: Other ifsym Symbols ¢ \FilledSectioningDiamond \Letter \Radiation \Fire ¤ \PaperLandscape ¡ \SectioningDiamond \Irritant £ \PaperPortrait ( \Telephone

: \StrokeOne ::: \StrokeThree ; \StrokeFive :: \StrokeTwo :::: \StrokeFour

47 7 Additional Information

Unlike the previous sections of this document, Section 7 does not contain new symbol tables. Rather, it provides additional help in using the Comprehensive LATEX Symbol List. First, it draws attention to symbol names used by multiple packages. Next, it provides some guidelines for ﬁnding symbols and gives some examples regarding how to construct missing symbols out of existing ones. Then, it comments on the spacing surrounding symbols in math mode. After that, it presents an ASCII and Latin 1 quick-reference guide, showing how to enter all of the standard ASCII/Latin 1 symbols in LATEX. And ﬁnally, it lists some statistics about this document itself.

7.1 Symbol Name Clashes Unfortunately, a number of symbol names are not unique; they appear in more than one package. Depending on how the symbols are defined in each package, LATEX will either output an error message or replace an earlier-defined symbol with a later-defined symbol. Table 181 presents a selection of name clashes that appear in this document. Using multiple symbols with the same name in the same document—or even merely loading conflicting symbol packages—can be tricky, but, as evidenced by the existence of Table 181, not impossible. The general procedure is to load the first package, rename the conflicting symbols, and then load the second package. Ex- amine the LATEX source for this document (symbols.tex)—especially the \savesymbol and \restoresymbol macros and their subsequent usage—to see one possible way to handle symbol conflicts. txfonts and pxfonts redefine a huge number of symbols—essentially, all of the symbols defined by latexsym, textcomp, the various AMS symbol sets, and LATEX 2ε itself. Similarly, mathabx redefines a vast number of math symbols in an attempt to improve their look. The txfonts, pxfonts, and mathabx conflicts are not listed in Table 181 because they are designed to be compatible with the symbols they replace. Table 182 on page 50 illustrates what “compatible” means in this context. To use the new txfonts/pxfonts symbols without altering the document’s main font, merely reset the default font families back to their original values after loading one of those packages:

\renewcommand\rmdefault{cmr} \renewcommand\sfdefault{cmss} \renewcommand\ttdefault{cmtt}

7.2 Where can I ﬁnd the symbol for ... ? If you can’t ﬁnd some symbol you’re looking for in this document, there are a few possible explanations:

The symbol isn’t intuitively named. As a few examples, the command to draw dice is “\Cube”; a plus sign with a circle around it (“exclusive or” to computer engineers) is “\oplus”; and lightning bolts in fonts designed by German speakers may have “blitz” in their names. The moral of the story is to be creative with synonyms when searching the index. The symbol is deﬁned by some package that I overlooked (or deemed unimportant). If there’s some symbol package that you think should be included in the Comprehensive LATEX Symbol List, please send me e-mail at the address listed on the title page. The symbol isn’t deﬁned in any package whatsoever.

Even in the last case, all is not lost. Sometimes, a symbol exists in a font, but there is no LATEX binding for it. For example, the PostScript Symbol font contains a “↵” symbol, which may be useful for representing a carriage return, but there is no package for accessing that symbol (as far as I know). To produce an unnamed symbol, you need to switch to the font explicitly with LATEX 2ε’s low-level font commands [LAT00] and use TEX’s primitive \char command [Knu86] to request a speciﬁc character number in the font.3

Symbols that do not exist in any font can sometimes be fabricated out of existing symbols. The LATEX 2ε source file fontdef.dtx contains a number of such definitions. For example, \models (see Table 40 on page 20) is defined in that file with:

\def\models{\mathrel|\joinrel=}

3pifont deﬁnes a convenient \Pisymbol command for accessing symbols in PostScript fonts by number. For example, “\Pisymbol{psy}{191}” produces “↵”.

48 Table 181: Symbol Name Clashes

Symbol LATEX 2ε AMS stmaryrd wasysym mathabx marvosym bbding ifsym dingbat wsuipa \baro < \bigtriangledown 5 ` \bigtriangleup 4 a \checkmark X D \Circle 5 \Cross # † * 49 \ggg ≫ Ï \Letter B \lightning

\Lightning E \lll ≪ Î \Rightarrow ⇒ ñ : \Square f 0 \Sun @ À \TriangleDown o 3 \TriangleUp n 1 Table 182: Example of a Benign Name Clash

Default txfonts Symbol (Computer Modern) (Times Roman)

R R R \textrecipe where \mathrel and \joinrel are used to control the horizontal spacing. (See The TEXbook [Knu86] for more information on those commands.) With some simple pattern-matching, one can easily deﬁne a backward \models sign (“=|”):

\def\ismodeledby{=\joinrel\mathrel|}

In general, arrows/harpoons, horizontal lines (“=”, “-”, “\relbar”, and “\Relbar”), and the various math- extension characters can be combined creatively with miscellaneous other characters to produce a variety of new symbols. Of course, new symbols can be composed from any set of existing characters. For instance, LATEX deﬁnes \hbar (“~”) as a bar character (\mathchar’26) followed by a backspace of 9 math units (\mkern-9mu), followed by the letter “h”:

\def\hbar{{\mathchar’26\mkern-9muh}}

We can just as easily deﬁne other barred letters:

\def\bbar{{\mathchar’26\mkern-9mu b}} \def\dbar{{\mathchar’26\mkern-12mu d}}

(The space after the “mu” is optional but is added for clarity.) \bbar and \dbar deﬁne “¯b” and “¯d”, respectively. Note that \dbar requires a greater backward math kern than \bbar; a -9 mu kern would have produced the less-attractive “¯d” glyph. To make composite symbols work properly within subscripts and superscripts, you may need to use TEX’s \mathchoice primitive. \mathchoice evaluates one of four expressions, based on whether the current math style is display, text, script, or scriptscript. (See The TEXbook [Knu86] for a more complete descrip- tion.) For example, the following LATEX code—posted to comp.text.tex by Torsten Bronger—composes a sub/superscriptable “⊥>” symbol out of \top and \bot (“>” and “⊥”):

\def\topbotatom#1{\hbox{\hbox to 0pt{$#1\bot$\hss}$#1\top$}} \newcommand*{\topbot}{\mathrel{\mathchoice{\topbotatom\displaystyle} {\topbotatom\textstyle} {\topbotatom\scriptstyle} {\topbotatom\scriptscriptstyle}}}

The following is another example that uses \mathchoice to construct symbols in diﬀerent math modes. The code deﬁnes a principal value integral symbol, which is an integral sign with a line through it.

\def\Xint#1{\mathchoice {\XXint\displaystyle\textstyle{#1}}% {\XXint\textstyle\scriptstyle{#1}}% {\XXint\scriptstyle\scriptscriptstyle{#1}}% {\XXint\scriptscriptstyle\scriptscriptstyle{#1}}% \!\int} \def\XXint#1#2#3{{\setbox0=\hbox{$#1{#2#3}{\int}$} \vcenter{\hbox{$#2#3$}}\kern-.5\wd0}} \def\ddashint{\Xint=} \def\dashint{\Xint-}

50 R R \dashint produces a single-dashed integral sign (“−”), while \ddashint produces a double-dashed one (“=”). The same technique can be used to produce, for example, clockwise and counterclockwise contour integrals. (Search the comp.text.tex archives for a post by Donald Arseneau that says exactly how.) The preceding code was taken verbatim from the UK TEX Users’ Group FAQ (http://www.tex.ac.uk/faq). Sometimes, however, amstext’s \text macro is all that is necessary to make composite symbols appear correctly in subscripts and superscripts, as in the following deﬁnitions of \neswarrow (“%.”) and \nwsearrow (“-&”):4

\newcommand{\neswarrow}{\mathrel{\text{$\nearrow$\llap{$\swarrow$}}}} \newcommand{\nwsearrow}{\mathrel{\text{$\nwarrow$\llap{$\searrow$}}}}

\text resembles LATEX’s \mbox command but shrinks its argument appropriately when used within a subscript or superscript. \llap (“left overlap”) and its counterpart, \rlap (“right overlap”), appear frequently when creating composite characters. \llap outputs its argument to the left of the current position, overlapping whatever text is already there. Similarly, \rlap overlaps whatever text would normally appear to the right of its argument. For example, “A\llap{B}” and “\rlap{A}B” each produce “AB”.However, the result of the former is the width of “A”, and the result of the latter is the width of “B”—\llap{... } and \rlap{... } take up zero space. As another example, fontdef.dtx composes the \ddots symbol (see Table 106 on page 33) out of three periods, raised 7 pt., 4 pt., and 1 pt., respectively:

\def\ddots{\mathinner{\mkern1mu\raise7\p@ \vbox{\kern7\p@\hbox{.}}\mkern2mu \raise4\p@\hbox{.}\mkern2mu\raise\p@\hbox{.}\mkern1mu}}

\p@ is a LATEX 2ε shortcut for “pt” or “1.0pt”. The remaining commands are deﬁned in The TEXbook [Knu86]. To draw a version of \ddots with the dots going along the opposite diagonal, we merely have to reorder the \raise7\p@, \raise4\p@, and \raise\p@:

\makeatletter \def\revddots{\mathinner{\mkern1mu\raise\p@ \vbox{\kern7\p@\hbox{.}}\mkern2mu \raise4\p@\hbox{.}\mkern2mu\raise7\p@\hbox{.}\mkern1mu}} \makeatother

(The \makeatletter and \makeatother commands are needed to coerce LATEX into accepting “@” as part of a macro name.) \revddots is essentially identical to the yhmath package’s \adots command. A more complex example of composing new symbols from existing symbols is the following deﬁnition of extensible \overbracket, \underbracket, \overparenthesis, and \underparenthesis symbols, taken from a comp.text.tex post by Donald Arseneau:

\makeatletter \def\overbracket#1{\mathop{\vbox{\ialign{##\crcr\noalign{\kern3\p@} \downbracketfill\crcr\noalign{\kern3\p@\nointerlineskip} $\hfil\displaystyle{#1}\hfil$\crcr}}}\limits} \def\underbracket#1{\mathop{\vtop{\ialign{##\crcr $\hfil\displaystyle{#1}\hfil$\crcr\noalign{\kern3\p@\nointerlineskip} \upbracketfill\crcr\noalign{\kern3\p@}}}}\limits} \def\overparenthesis#1{\mathop{\vbox{\ialign{##\crcr\noalign{\kern3\p@} \downparenthfill\crcr\noalign{\kern3\p@\nointerlineskip} $\hfil\displaystyle{#1}\hfil$\crcr}}}\limits} \def\underparenthesis#1{\mathop{\vtop{\ialign{##\crcr $\hfil\displaystyle{#1}\hfil$\crcr\noalign{\kern3\p@\nointerlineskip} \upparenthfill\crcr\noalign{\kern3\p@}}}}\limits} \def\downparenthfill{$\m@th\braceld\leaders\vrule\hfill\bracerd$} \def\upparenthfill{$\m@th\bracelu\leaders\vrule\hfill\braceru$} \def\upbracketfill{$\m@th\makesm@sh{\llap{\vrule\@height3\p@\@width.7\p@}}% \leaders\vrule\@height.7\p@\hfill

4Note that if your goal is to typeset commutative diagrams, then you probably want to use XY-pic.

51 \makesm@sh{\rlap{\vrule\@height3\p@\@width.7\p@}}$} \def\downbracketfill{$\m@th \makesm@sh{\llap{\vrule\@height.7\p@\@depth2.3\p@\@width.7\p@}}% \leaders\vrule\@height.7\p@\hfill \makesm@sh{\rlap{\vrule\@height.7\p@\@depth2.3\p@\@width.7\p@}}$} \makeatother

Table 183 showcases these accents. The TEXbook [Knu86] or another book on TEX primitives is indispensible for understanding how the preceding code works. The basic idea is that \downparenthfill, \upparenthfill, \downbracketfill, and \upbracketfill do all of the work; they output a left symbol (e.g., \braceld [“z”] for \downparenthfill), a horizontal rule that stretches as wide as possible, and a right symbol (e.g., \bracerd [“{”] for \downparenthfill). \overbracket, \underbracket, \overparenthesis, and \underparenthesis merely create a table whose width is determined by the given text, thereby constraining the width of the horizontal rules.

Table 183: Manually Composed Extensible Accents z { abc \overbracket{abc} abc \overparenthesis{abc}

abc \underbracket{abc} |abc} \underparenthesis{abc}

Accents are a special case of combining existing symbols to make new symbols. While various tables in this document show how to add an accent to an existing symbol, some applications, such as transliterations from non-Latin alphabets, require multiple accents per character. For instance, the creator of pdfTEX writes his name as “HànThêThành”.´ The wsuipa package defines \diatop and \diaunder macros for putting one or more diacritics or accents above or below a given character. For example, \diaunder[{\diatop[\’|\=]}| \textsubdot{r}] produces “¯´r”. See the wsuipa documentation for more information.

The accents package facilitates the fabrication of accents in math mode. Its \accentset command en- ? ables any character to be used as an accent. For instance, \accentset{\star}{f} produces “f ” and e \accentset{e}{X} produces “X”. \underaccent does the same thing, but places the accent beneath the character. This enables constructs like \underaccent{\tilde}{V}, which produces “V ”. accents provides other accent-related features as well; see the documentation for more information. ˜

7.3 Math-mode spacing Terms such as “binary operators”, “relations”, and “punctuation” in Section 3 primarily regard the surrounding spacing. (See the Short Math Guide for LATEX [Dow00] for a nice exposition on the subject.) To use an symbol for a diﬀerent purpose, you can use the TEX commands \mathord, \mathop, \mathbin, \mathrel, \mathopen, \mathclose, and \mathpunct. For example, if you want to use \downarrow as a variable (an “ordinary” symbol) instead of a delimiter, you can write “$3 x + \mathord{\downarrow}$” to get the properly spaced “3x + ↓” rather than the awkward-looking “3x+ ↓”. See The TEXbook [Knu86] for more information. The purpose of the “log-like symbols” in Tables 79 and 80 is to provide the correct amount of spacing around and within multiletter function names. Table 184 contrasts the output of the log-like symbols with various, na¨ıve alternatives. In addition to spacing, the log-like symbols also handle subscripts properly. For example, “\max_{p \in P}” produces “maxp∈P ” in text, but “max” as part of a displayed formula. p∈P

Table 184: Spacing Around/Within Log-like Symbols

LATEX expression Output $r \sin \theta$ r sin θ (best) $r sin \theta$ rsinθ $r \mbox{sin} \theta$ rsinθ

The amsmath package makes it straightforward to deﬁne new log-like symbols:

52 \DeclareMathOperator{\atan}{atan} \DeclareMathOperator*{\lcm}{lcm}

The diﬀerence between \DeclareMathOperator and \DeclareMathOperator* involves the handling of subscripts. With \DeclareMathOperator*, subscripts are written beneath log-like symbols in display style and to the right in text style. This is useful for limit operators (e.g., \lim) and functions that tend to map over a set (e.g., \min). In contrast, \DeclareMathOperator tells TEX that subscripts should always be displayed to the right of the operator, as is common for functions that take a single parameter (e.g., \log and \cos). Table 185 contrasts symbols declared with \DeclareMathOperator and \DeclareMathOperator* in both text style ($...$) and display style (\[...\]).

Table 185: Deﬁning new log-like symbols

Declaration function $\newlogsym {p \in P}$ \[ \newlogsym {p \in P} \]

\DeclareMathOperator newlogsymp∈P newlogsymp∈P

\DeclareMathOperator* newlogsymp∈P newlogsym p∈P

7.4 ASCII and Latin 1 quick reference Table 186 on the following page amalgamates data from various other tables in this document into a convenient reference for LATEX 2ε typesetting of ASCII characters, i.e., the characters available on a typical5 computer keyboard. The ﬁrst two columns list the character’s ASCII code in decimal and hexadecimal. The third column shows what the character looks like. The fourth column lists the LATEX 2ε command to typeset the character as a text character. And the fourth column lists the LATEX 2ε command to typeset the character within a \texttt{...} command (or, more generally, when \ttfamily is in eﬀect). The following are some additional notes about the contents of Table 186:

" is not available in the OT1 font encoding.

The characters “<”, “>”, and “|” do work as expected in math mode, although they produce, respectively, “¡”, “¿”, and “—” in text mode.6 Hence, $<$, $>$, and $|$ serve as a terser alternative to \textless, \textgreater, and \textbar. Note that for typesetting metavariables many people prefer \textlangle and \textrangle to \textless and \textgreater, i.e., “hfilenamei” instead of “<filename>”. The various \char commands within \texttt are necessary only in the OT1 font encoding. In other encodings (e.g., T1), commands such as \{, \}, \_, and \textbackslash all work properly. \textasciicircum can be used instead of \^{}, and \textasciitilde can be used instead of \~{}. For typesetting tildes in URLs and Unix filenames, some people prefer \sim (see Table 40 on page 20), which produces a larger symbol. However, a superior approach for typesetting URLs is to use the url package, which has a number of additional nice features. The IBM version of ASCII characters 1 to 31 can be typeset using the ascii package. See Table 132 on page 38.

To replace ‘ and ’ with the more computer-like (and more visibly distinct) ` and ' within a verbatim environment, use the upquote package. Outside of verbatim, you can use \char18 and \char13 to get the modiﬁed quote characters. (The former is actually a grave accent.)

Similar to Table 186, Table 187 on page 55 is an amalgamation of data from other tables in this document. While Table 186 shows how to typeset the 7-bit ASCII character set, Table 187 shows the Latin 1 (Western European) character set, also known as ISO-8859-1. The following are some additional notes about the contents of Table 187:

5typical for the United States, at least 6Donald Knuth didn’t think such symbols were important outside of mathematics, so he omitted them from the OT1 font encoding.

53 Table 186: LATEX 2ε ASCII Table

Dec Hex Char Body text \texttt Dec Hex Char Body text \texttt 33 21 ! !! 62 3E > \textgreater > 34 22 " \textquotedbl " 63 3F ? ?? 35 23 # \# \# 64 40 @ @@ 36 24 $ \$ \$ 65 41 A AA 37 25 % \% \% 66 42 B BB 38 26 & \& \& 67 43 C CC . . . . . 39 27 ’ ’’ . . . . . 40 28 ( (( 90 5A Z ZZ 41 29 ) )) 91 5B [ [[ 42 2A * ** 92 5C \ \textbackslash \char‘\\ 43 2B + + + 93 5D ] ]] 44 2C , ,, 94 5E ˆ \^{} \^{} 45 2D - -- 95 5F \_ \char‘\_ 46 2E . .. 96 60 ‘ ‘‘ 47 2F / // 97 61 a a a 48 30 0 0 0 98 62 b b b 49 31 1 1 1 99 63 c c c . . . . . 50 32 2 2 2 ...... 122 7A z z z 57 39 9 9 9 123 7B { \{ \char‘\{ 58 3A : :: 124 7C | \textbar | 59 3B ; ;; 125 7D } \} \char‘\} 60 3C < \textless < 126 7E ˜ \~{} \~{} 61 3D = = =

A “(tc)” after a symbol name means that the textcomp package must be loaded to access that symbol. A “(T1)” means that the symbol requires the T1 font encoding. The fontenc package can change the font encoding document-wide.

Many of the \text. . . accents can also be produced using the accent commands shown in Table 11 on page 10 plus an empty argument. For instance, \={} is essentially the same as \textasciimacron.

The commands in the “LATEX 2ε” columns work both in body text and within a \texttt{...} command (or, more generally, when \ttfamily is in eﬀect). Microsoft® Windows® normally uses a superset of Latin 1 called “CP1252” (Code Page 1252). CP1252 adds codes in the range 128–159 (hexadecimal 80–9F), including characters such as dashes, daggers, and quotation marks. If there’s suﬃcient interest, a future version of the Comprehensive LATEX Symbol List may include a CP1252 table.

While too large to incorporate into this document, a listing of ISO 8879:1986 SGML/XML character entities and their LATEX equivalents is available from http://www.bitjungle.com/~isoent/. Some of the characters presented there make use of isoent, a LATEX 2ε package (available from the same URL) that fakes some of the missing ISO glyphs using the LATEX picture environment.7

7.5 About this document History David Carlisle wrote the ﬁrst version of this document in October, 1994. It originally contained all of the native LATEX symbols (Tables 25, 33, 40, 63, 79, 81, 93, 94, 98, 101, 109, and a few tables that have since been reorganized) and was designed to be nearly identical to the tables in Chapter 3 of Leslie Lamport’s book [Lam86]. Even the table captions and the order of the symbols within each table matched! The AMS

7isoent is not featured in this document, because it is not available from CTAN and because the faked symbols are not “true” characters; they exist in only one size, regardless of the body text’s font size.

54 Table 187: LATEX 2ε Latin 1 Table

Dec Hex Char LATEX 2ε Dec Hex Char LATEX 2ε 161 A1 ¡ !‘ 209 D1 N˜ \~{N} 162 A2 ¢ \textcent (tc) 210 D2 O` \‘{O} £ 163 A3 \pounds 211 D3 O´ \’{O} ¤ 164 A4 \textcurrency (tc) 212 D4 Oˆ \^{O} ¥ (tc) 165 A5 \textyen 213 D5 O˜ \~{O} 166 A6 ¦ \textbrokenbar (tc) 214 D6 O¨ \"{O} 167 A7 § \S 215 D7 Ö \texttimes (tc) 168 A8 ¨ \textasciidieresis (tc) © 216 D8 Ø \O 169 A9 \textcopyright ` ª 217 D9 U \‘{U} 170 AA \textordfeminine ´ 171 AB \guillemotleft (T1) 218 DA U \’{U} ˆ 172 AC ¬ \textlnot (tc) 219 DB U \^{U} ¨ 174 AE ® \textregistered 220 DC U \"{U} 175 AF ¯ \textasciimacron (tc) 221 DD Y´ \’{Y} 176 B0 ° \textdegree (tc) 222 DE Þ \TH (T1) 177 B1 ± \textpm (tc) 223 DF ß \ss 178 B2 ² \texttwosuperior (tc) 224 E0 à \‘{a} 179 B3 ³ \textthreesuperior (tc) 225 E1 á \’{a} 180 B4 ´ \textasciiacute (tc) 226 E2 â \^{a} 181 B5 µ \textmu (tc) 227 E3 ã \~{a} 182 B6 ¶ \P 228 E4 ä \"{a} 183 B7 · \textperiodcentered 229 E5 ˚a \aa 184 B8 ¸ \c{} 230 E6 æ \ae 185 B9 ¹ \textonesuperior (tc) 231 E7 ¸c \c{c} 186 BA º \textordmasculine 232 E8 è \‘{e} 187 BB \guillemotright 233 E9 é \’{e} 188 BC ¼ \textonequarter (tc) 234 EA ê \^{e} 189 BD ½ \textonehalf (tc) 235 EB ë \"{e} 190 BE ¾ \textthreequarters (tc) 236 EC `ı \‘{ı} 191 BF ¿ ?‘ 237 ED ´ı \’{ı} 192 C0 A` \‘{A} 238 EE ˆı \^{ı} 193 C1 A´ \’{A} 239 EF ¨ı \"{ı} ð 194 C2 Aˆ \^{A} 240 F0 \dh (T1) 241 F1 ñ \~{n} 195 C3 A˜ \~{A} 242 F2 ò \‘{o} 196 C4 A¨ \"{A} 243 F3 ó \’{o} A˚ 197 C5 \AA 244 F4 ô \^{o} Æ 198 C6 \AE 245 F5 õ \~{o} Ç 199 C7 \c{C} 246 F6 ö \"{o} ` 200 C8 E \‘{E} 247 F7 ö \textdiv (tc) ´ 201 C9 E \’{E} 248 F8 ø \o 202 CA Eˆ \^{E} 249 F9 ù \‘{u} 203 CB E¨ \"{E} 250 FA ú \’{u} 204 CC Ì \‘{I} 251 FB û \^{u} 205 CD Í \’{I} 252 FC ü \"{u} 206 CE Î \^{I} 253 FD ý \’{y} þ 207 CF Ï \"{I} 254 FE \th (T1) 208 D0 Ð \DH (T1) 255 FF ÿ \"{y}

55 symbols (Tables 26, 41, 42, 66, 67, 82, 85, 90, and 110) and an initial Math Alphabets table (Table 118) were added thereafter. Later, Alexander Holt provided the stmaryrd tables (Tables 27, 35, 43, 69, 76, and 91). In January, 2001, Scott Pakin took responsibility for maintaining the symbol list and has since implemented a complete overhaul of the document. The result, now called, “The Comprehensive LATEX Symbol List”, includes the following new features:

the addition of a handful of new math alphabets, dozens of new font tables, and thousands of new symbols the categorization of the symbol tables into body-text symbols, mathematical symbols, science and technology symbols, dingbats, and other symbols, to provide a more user-friendly document structure an index, table of contents, and a frequently-requested symbol list, to help users quickly locate symbols symbol tables rewritten to list the symbols in alphabetical order

appendices to provide additional information relevant to using symbols in LATEX tables showing how to typeset all of the characters in the ASCII and Latin 1 font encodings

Furthermore, the internal structure of the document has been completely altered from David’s original version. Most of the changes are geared towards making the document easier to extend, modify, and reformat.

Build characteristics Table 188 lists some of this document’s build characteristics. Most important is the list of packages that LATEX couldn’t find, but that symbols.tex otherwise would have been able to take advantage of. Complete, prebuilt versions of this document are available from CTAN (http://www.ctan.org/ or one of its many mirror sites) in the directory tex-archive/info/symbols/comprehensive. Table 189 shows the package date (specified in the .sty file with \ProvidesPackage) for each package that was used to build this document and that specifies a package date. Packages are not listed in any particular order in either Table 188 or 189.

Table 188: Document Characteristics Characteristic Value Source ﬁle: symbols.tex Build date: October 8, 2002 Symbols documented: 2590 Packages included: textcomp latexsym amssymb stmaryrd euscript wasysym pifont mathcomp marvosym manfnt bbding ifsym tipa wsuipa ulsy ar txfonts mathabx fclfont ascii dingbat skull eurosym esvect yfonts yhmath esint accents mathrsfs zapfchan bbold dsfont bbm Packages omitted: none

56 Table 189: Package versions used in the preparation of this document

Name Date textcomp 2000/08/30 latexsym 1998/08/17 amssymb 1996/11/03 stmaryrd 1994/03/03 euscript 1995/01/06 wasysym 1999/05/13 pifont 2000/01/12 marvosym 2000/05/01 manfnt 1999/07/01 bbding 1999/04/15 ifsym 2000/04/18 tipa 2001/12/31 txfonts 2000/12/15 dingbat 2001/04/27 skull 2002/01/23 eurosym 1998/08/06 yfonts 1999/05/12 accents 2000/08/06

References

[Dow00] Michael Downes. Short math guide for LATEX, July 19, 2000. Version 1.07. Available from http:// www.ams.org/tex/short-math-guide.html.

[Knu86] Donald E. Knuth. The TEXbook, volume A of Computers and Typesetting. Addison-Wesley, Reading, MA, USA, 1986.

[Lam86] Leslie Lamport. LATEX: A document preparation system. Addison-Wesley, Reading, MA, USA, 1986. [LAT98] LATEX3 Project Team. A new math accent. LATEX News. Issue 9, June 1998. Available from http://www.ctan.org/tex-archive/macros/latex/doc/ltnews09.pdf (also included in many TEX distributions).

[LAT00] LATEX3 Project Team. LATEX 2ε font selection, January 30, 2000. Available from http:// www.ctan.org/tex-archive/macros/latex/doc/fntguide.ps (also included in many TEX distributions).

57 Index

If you’re having trouble locating a symbol, try looking under “T” for “\text...”. Many text-mode commands begin with that prefix. Also, accents are shown over/under a black box, e.g., “ á ” for “\’”. Some symbol entries appear to be listed repeatedly. This happens when multiple packages define identical (or nearly identical) glyphs with the same symbol name.8

Symbols AMS 6, 14, 15, 18, 20, 22–25, 28, \ArrowBoldUpRight (x) . . . 39 \" (ä) ...... 10 29, 31–33, 48, 54 \Arrownot () ...... 27 \# (#) ...... 7, 54 amsfonts (package) 15, 20, 22, 25, \arrownot ()Y ...... 27 \$ ($) ...... 7, 54 33, 35 arrows . . .X . . . . . 25, 26, 39, 48 \% (%) ...... 7, 54 amsmath (package) . . 6, 28, 52 double-headed, diagonal 51 \& (&) ...... 7, 54 amssymb (package) 6, 15, 20, 22, extensible ...... 31, 32 \’ (á) ...... 10 25, 33, 35, 56–58 negatedw ...... 25, 26 w ( (() ...... 30 amstext (package) ...... 51 \Arrowvert (?) ...... 30 ) ()) ...... 30 ? \anchor (O) ...... 43 \arrowvert ( ) ...... 30 * (*) ...... 17 and ...... see \wedge Arseneau, Donald ...... 51 \. (˙a) ...... 10 \angle ( ) ...... 33 ASCII ...... 6, 7, 38, 53, 56 / (/) ...... 30 ∠ \angle (6 ) ...... 33 table ...... 54 [ ([) ...... 30 ascii (package) ...... 38, 53, 56 \Anglesign (W) ...... 34 ] (]) ...... 30 \ascnode ( ) ...... 36 \Ankh (ˆ) ...... 46 \^ (â) ...... 10 APL aspect ratio ...... 36 ¦ \^{} (ˆ) ...... 53 modifiers ...... 37 \ast ( ) ...... 17 (∗) ...... 15 \_ ( ) ...... 7, 53 symbols ...... 37 \ast \Asterisk (¦) ...... 17 \‘ (à) ...... 10 \APLbox ( ) ...... 37 \~ (ã) ...... 10 (N) ...... 41 \APLcirc ~(◦) ...... 37 \Asterisk ¦ \~{} (˜) ...... 53 \APLcomment ( ) ...... 37 \asterisk ( ) ...... 17 A \APLdown ( ) ...... 37 \AsteriskBold ( ) ...... 41 A \APLdownarrowboxF ( ) . . . . 37 \AsteriskCenterOpen (B) . . 41 a (esvect package option) . . . 32 \APLinput ( ) . . .o ...... 37 \AsteriskRoundedEnds (X) . 41 ˚ \AA (A) ...... 7 \APLinv (÷)} ...... 37 asterisks ...... 17, 41, 42 \aa (˚a)...... 7 \APLleftarrowbox ( ) . . . . 37 ~ \AsteriskThin (C) ...... 41 abzüglich . . see \textdiscount \APLlog ( ) . . . . .p ...... 37 \AsteriskThinCenterOpen (D) \AC ( ) ...... 36 \APLminus(−) ...... 37 ...... 41 accents¬ 10–12, 31, 32, 37, 51–52 \APLnot (∼) ...... 37 astrological symbols ...... 37 any character as ...... 52 \APLrightarrowbox ( ) . . . . 37 astronomical symbols . . . 36, 37 extensible . . 31, 32, 51–52 \APLstar ( ) ...... 37 q \astrosun ( ) ...... 36 multiple per character . 52 ( ) ...... 37 \APLup E \asymp () ...... 20 accents (package) . . . . 52, 56, 57 \APLuparrowbox ( ) ...... 37 \atan (atan) ...... 53 \accentset ...... 52 \APLvert ( | ) . . .n ...... 37 \ataribox ( ) ...... 45 \ACK (♠) ...... 38 \apprge ( ) ...... 23 \AtForty (Øm ) ...... 46 \acute (´) ...... 31 \apprle ( ) ...... 23 ? \AtNinetyFive (Ó) ...... 46 . \approx (>≈) ...... 20 \adots (.. ) ...... 33, 51 atomic math objects . . . 27, 28 \approxeq (u) ...... 20 \AtSixty ( ) ...... 46 \AE (Æ) ...... 7 Õ \Aquarius (ê) ...... 37 \ae (æ) ...... 7 \aquarius ( ) ...... 37 B \agemO ( ) ...... 34 \AR (A) ...... 36 \B ...... 8 s e \ain ( )0 ...... 12 ar (package) ...... 36, 56 b (esvect package option) . . . 32 \aleph (ℵ) ...... 29, 33 \arccos (arccos) ...... 27 \b (a) ...... 10 ¯ \alpha (α) ...... 28 \arcsin (arcsin) ...... 27 \babygamma (!) ...... 10 alphabets \arctan (arctan) ...... 27 \backepsilon () ...... 20 African ...... 8 \arg (arg) ...... 27 \backprime (8) ...... 33 Greek ...... 28 \Aries (P) ...... 37 \backsim (v) ...... 20 Hebrew ...... 29 \Aries (à) ...... 37 \backsimeq (w) ...... 20 math ...... 35 \aries ( ) ...... 37 \backslash (\) ...... 30, 33 phonetic ...... 8–10 \ArrowBoldDownRight (y) . 39 \bar (¯) ...... 31 \alphaup (α) ...... 28 \barb (¦) ...... 10 \ArrowBoldRightCircled ({) 39 alpine symbols ...... 47 \bard () ...... 10 z \amalg (q) ...... 15 \ArrowBoldRightShort ( ) . . 39 \bari (') ...... 10 ampersand ...... see \& \ArrowBoldRightStrobe (w) 39 \barin (V) ...... 29

8This occurs frequently with amssymb and mathabx.

58 \barl (.) ...... 10 \bigcurlyvee ( ) ...... 18 blackboard bold see alphabets, Þ \barleftharpoon ( ) . . . . . 27 \bigcurlyvee (b) ...... 18 math \baro ( vs. <) ...... 49 \bigcurlywedge ( ) ...... 18 \blackdiamond ( ) ...... 17

\baro ( ) ...... 16 \bigcurlywedge (c) ...... 18 \blacklozenge () ...... 33 < \baro ( ) ...... 10 \BigDiamondshape (&) . . . . 42 \blacksmiley ( ) ...... 45 \barp (A) ...... 10 \blacksquare ( ) ...... 33 \BigHBar () ...... 42 - barred letters ...... 50 \blacktriangle ( ) ...... 33 \biginterleave ( ) ...... 18 N \barrightharpoon (ß) . . . . 27 g \blacktriangledown () . . . 17 \BigLowerDiamond (_) . . . . 42 \barsci (+) ...... 10 \blacktriangledown (H) . . . 33 \barscu (X) ...... 10 \bignplus ( )Æ ...... 18 \blacktriangleleft () . . . 17 \bigoasterisk ( ) ...... 18 \baru (T) ...... 10 Î \blacktriangleleft (J) . . . 24 \barwedge (X) ...... 17 \bigobackslashË ( ) ...... 18 \blacktriangleright () . . 17 \bigobot ( ) ...... 18 \barwedge (Z) ...... 15 Å \blacktriangleright (I) . . 24 \bigocirc ( ) ...... 18 \Bat (ý) ...... 46 Ç \blacktriangleup ( ) . . . . . 17 ( ) . . . . . 18 \bbalpha ( ) ...... 35 \bigocoasteriskÃ \Bleech (Ë) ...... 46 \bbar (¯b) ...... 50 \bigodiv (J) ...... 18 \blitza (©) ...... 15, 27 \bbbeta ( ) ...... 35 \bigodot ( È) ...... 17 \blitzb ( ) ...... 27 \bigoleft ( ) ...... 18 \Bbbk (k) ...... 29 Á \blitzc ( ) ...... 27 bbding (package) . 39–41, 43, 44, \bigominus L( ) ...... 18 \blitzd ( ) ...... 27 49, 56, 57 \bigoplus ( É) ...... 17 \blitze ( ) ...... 27 \bbgamma ( ) ...... 35 \bigoright (Í) ...... 18 \bmod ...... 27 bbgreekl (mathbbol package op- \bigoslash (N) ...... 18 body-text symbols ...... 7–14 tion) ...... 35 \bigotimesÊ( ) ...... 17 \bot (⊥) ...... 15, 29, 50 bbm (package) ...... 35, 56 \bigotop ( ) . . .Ï ...... 18 \botdoteq () ...... 21 bbold (package) ...... 35, 56 \bigotriangleupÌ ( ) . . . . . 18 \Bouquet (¥) ...... 46 \bbslash ( ) ...... 16 \bigovoid ( ) ...... 18 \Bowtie ( ) ...... 45 \bigparallel ( ) ...... 18 \bowtie (./) ...... 20 \Beam (") ...... 38 f 1 \bigplus ( ) ...... 18 \Box ( ) ...... 33, 34 \Bearing (#) ...... 38 \because ( ) ...... 20 \BigRightDiamond (/) . . . . 42 \boxast (i) ...... 16 ∵ f \BEL (•) ...... 38 \bigsqcap ( ) ...... 18 \boxasterisk ( ) ...... 17 n \bell ( ) ...... 45 \bigsqcap ( ) ...... 18 \boxbackslash ( ) ...... 17 \beta (β) ...... 28 \bigsqcapplus ( ) ...... 19 \boxbar (k) ...... 16 F k \betaup (β) ...... 28 \bigsqcup ( ) ...... 17 \boxbot ( ) ...... 17 \boxbox ( ) ...... 16 \beth (i) ...... 29 \bigsqcupplus () ...... 19 \boxbslash (j) ...... 16 \between ( ) ...... 21 \BigSquare ( ) ...... 42 \boxcirc (e) ...... 17 \between (G) ...... 20 \bigsquplus ( ) ...... 18 \boxcircle ( ) ...... 16 \Bicycle (®) ...... 43 \bigstar () ...... 17 ¦ \boxcoasterisk (g) ...... 17 \bigast ( ) ...... 17 ( ) ...... 33 \bigstar F \boxdiv (c) ...... 17 \bigbox (e) . . . .Ö ...... 18 \bigtimes ( ) ...... 18 \boxdot (d) ...... 17 \bigboxasterisk ( Þ) . . . . . 18 \BigTriangleDown (#) . . . . 42 \boxdot ( ) ...... 15, 16 \bigboxbackslashÛ ( ) . . . . 18 \bigtriangledown (`) . . . . 18 \boxdotLeft () ...... 26 \bigboxbot ( Õ) ...... 18 \bigtriangledown (5 vs. `) 49 \boxdotleft () ...... 26 \bigboxcirc ( ) . .× ...... 18 \bigtriangledown (5) . . . . 15 \boxdotRight () ...... 26 \bigboxcoasteriskÓ ( ) . . . 18 \BigTriangleLeft (") . . . . 42 \boxdotright () ...... 26 \bigboxdiv (Ô) ...... 18 $ \boxempty ( ) ...... 16 \bigboxdot ( Ø) ...... 18 \BigTriangleRight ( ) . . . 42 \boxLeft ( ) ...... 26 \bigboxleft ( ) ...... 18 \BigTriangleUp (!) ...... 42 Ñ \boxleft (h) ...... 17 \bigboxminus Ð( ) ...... 18 \bigtriangleup ( ) ...... 18 a \boxleft () ...... 26 \bigboxplus ( ) ...... 18 \bigtriangleup (4 vs. ) . 49 Ù a \boxminus (a) ...... 17 \bigboxright ( ) ...... 18 (4) ...... 15 Ý \bigtriangleupU \boxminus ( ) ...... 15 \bigboxslash ( ) ...... 18 Ò \biguplus ( ) ...... 17 \boxplus (`) ...... 17 \bigboxtimesÚ( ) ...... 18 \bigvarstar () ...... 17 \boxplus () ...... 15 \bigboxtop ( ) ...... 18 ß \BigVBar W( ) ...... 42 \boxRight () ...... 26 \bigboxtriangleup ( ) . . . 18 Ü \bigvee ( )V ...... 17 \boxright (i) ...... 17 \bigboxvoid ( ) ...... 18 T \bigwedge ( ) ...... 17 \boxright () ...... 26 \bigcap ( ) ...... 17 \binampersand ( ) ...... 16 \boxslash (m) ...... 17 \bigcirc ( ) ...... 15 N binary operators ...... 15–17 \boxslash (l) ...... 16 % \BigCircle ( ) ...... 42 binary relations ...... 20–24 \boxtimes (b) ...... 17 \bigcoast (§) ...... 17 negated ...... 20–22 \boxtimes () ...... 15 \bigcomplementop ( ) . . . . . 18 \bindnasrepma ( ) ...... 16 \boxtop (j) ...... 17 O \BigCrossS( ) ...... 42 \Biohazard (h) ...... 38 \boxtriangleup (o) ...... 17 \bigcup ( ) ...... 17 biological symbols ...... 38 \boxvoid (l) ...... 17

59 \boy (D ) ...... 37 \Circle (5) ...... 42 \Colonapprox () ...... 21 \braceld (z) ...... 52 \Circle ( vs. 5) ...... 49 \colonapprox ( ) ...... 21 ({) ...... 52 \bracerd > \Circle (#) ...... 45 \Coloneq (H) ...... 21 > \bracevert (>) ...... 30 \circlearrowleft# (ö) . . . . 26 \coloneq ( ) ...... 21 ( ) ...... 21 braket (package) ...... 30 \circlearrowleft ( ) . . . . 25 \coloneq D \breve (˘) ...... 31 \circlearrowright (÷) . . . . 26 \Coloneqq (F) ...... 21 ( ) ...... 15, 21 \brokenvert () ...... 45 \circlearrowright () . . . . 25 \coloneqq B \Colonsim ( ) ...... 21 Bronger, Torsten| ...... 50 circled numbers ...... 41 \colonsim ( ) ...... 21 \BS () ...... 38 \CircledA (ª) ...... 46 communication symbols . . . . 38 \BSEfree (n) ...... 38 \circledast (~) ...... 15 \bullet (•) ...... 15 \circledbar (V) ...... 16 comp.text.tex (newsgroup) . 6, \Bumpedeq () ...... 21 \circledbslash (W) ...... 16 15, 50, 51 \complement (A) ...... 29 \bumpedeq () ...... 21 \circledcirc (}) ...... 15 \complement ( ) ...... 29 \Bumpeq (m) ...... 20 \circleddash () ...... 15 { complex numbers (C).... see \bumpeq (l) ...... 20 \circleddot ...... see \odot \circleddotleft () . . . . 26 alphabets, math C \circleddotright () . . . . 26 Comprehensive TEX Archive Net- c (esvect package option) . . . 32 \circledgtr (S) ...... 21 work ...... 1, 6, 54, \c (¸a) ...... 10, 55 \circledless (R) ...... 21 56 \CAN (↑) ...... 38 \circledminus ... see \ominus computer hardware symbols . 37 \Cancer (ã) ...... 37 \circledotleft ...... see \ComputerMouse (Í) ...... 37 \cancer ( ) ...... 37 \circleddotleft \cong () ...... 20 \Cap (e)_ ...... 15 \circledotright ...... see \conjunction ( ) ...... 37 \cap (X) ...... 17 \circleddotright contradiction symbolsV . . 15, 27 \cap (∩) ...... 15 \circledplus ..... see \oplus control characters ...... 38 \convolution ( ) ...... 17 \Capricorn (é) ...... 37 \circledR (r) ...... 14, 29 ` \capricornus ( ) ...... 37 \circledS ( ) ...... 29 \coprod ( ) ...... 17 s © card suits . . .d ...... 33, 34, 44 \circledslash ... see \oslash \copyright ( ) ...... 7 k cardinality ...... see \aleph \circledtimes ... see \otimes \corner ( ) ...... 12 caret ...... see \^ \circledvee (U) ...... 16 \Corresponds (=) ...... 34 Carlisle, David ...... 1, 54 \circledwedge (T) ...... 16 \corresponds ( ) ...... 21 carriage return ...... 38, 48 \circleleft () ...... 26 \cos (cos) ...... 27, 53 C \carriagereturn ( ) . . . . . 43 \circleright () ...... 26 \cosh (cosh) ...... 27 \cdot (·) ...... 15 circles ...... 42, 43, 45 \cot (cot) ...... 27 \cdotp (·) ...... 33 \coth (coth) ...... 27 \CircleShadow (d) ...... 43 \cdots (···) ...... 33 Courier ...... 13 a Cedi . see \textcolonmonetary \CircleSolid ( ) ...... 43 CP1252 ...... 54 cedilla ...... see accents \Circpipe (›) ...... 38 \CR (♪) ...... 38 \circplus (¨) ...... 17 \Celtcross (‡) ...... 46 \Cross () ...... 42 \cent ( ) ...... 13 \Circsteel (•) ...... 38 \Cross ( vs. * vs. ) . . . . . 49 \centerdot ( ) ...... 17 circumﬂex ...... see accents † ¢ \Cross ( ) ...... 46 \centerdot ( ) ...... 15 \CleaningA («) ...... 46 † * cents ...... see \textcent \CleaningF (¾) ...... 46 \Cross ( ) ...... 40 \CleaningFF ( ) ...... 46 \crossb (¥) ...... 10 \CEsign (C) ...... 38 ¿ \changenotsign ...... 22 \CleaningP (¬) ...... 46 \CrossBoldOutline (-) . . . . 40 ( ) ...... 46 \char ...... 6,48 \CleaningPP \CrossClowerTips (4) . . . . 40 (;) ...... 10 \check (ˇ) ...... 31 \clickb \crossd ( ) ...... 10 ( ) ...... 10 check marks ...... 40, 41, 43 \clickc \Crossedbox ( ) ...... 43 R X \checked ( ) ...... 45 \clickt ( ) ...... 10 crosses ...... 40, 46 \clock ( ) ...... 45 \CheckedBox ( ) ...... 41 \crossh (#) ...... 10 clock symbols ...... 47 \Checkedbox (V2) ...... 43 (.) ...... 40 \Clocklogo ( ) ...... 43 \CrossMaltese \Checkmark (!) ...... 40 U (3) ...... 10 \closedniomega (?) ...... 10 \crossnilambda \checkmark ( ) ...... 14 X \closedrevepsilon () . . . . 10 \CrossOpenShadow (+) . . . . . 40 D \checkmark (X vs. ) . . . . . 49 \Cloud () ...... 46 \CrossOutline (,) ...... 40 \checkmark (D) ...... 43 clovers ...... 41, 42 cruciﬁxes ...... 40, 46 \CheckmarkBold (") ...... 40 clubs (suit) ...... 33, 34, 44 \csc (csc) ...... 27 \chi (χ) ...... 28 \clubsuit (♣) ...... 33 CTAN see Comprehensive TEX \chiup (χ)...... 28 \coAsterisk (§) ...... 17 Archive Network \circ (◦) ...... 15 \coasterisk (§) ...... 17 \Cube ...... 47, 48 \circeq () ...... 21 \Coffeecup (K) ...... 43 cube root ...... see \sqrt \circeq ($) ...... 20 \colon ...... 33 \Cup (d) ...... 15 \CIRCLE ( ) ...... 45 \colon (:) ...... 33 \cup (Y) ...... 17

60 ... \cup (∪) ...... 15 \dddot ( ) ...... 31 Mayan ...... 34 \curlyc ( ) ...... 10 \ddot (¨) ...... 31 old-style ...... 13 \curlyeqprec (¶) ...... 21 . segmented ...... 36 \ddots ( ..) ...... 33, 51 \curlyeqprec (2) ...... 20 \dim (dim) ...... 27 \curlyeqsucc (·) ...... 21 \DeclareMathOperator . . . . 53 \ding ...... 8, 39–44 \DeclareMathOperator* . . . 53 \curlyeqsucc (3) ...... 20 dingautolist ...... 41 \curlyesh (N) ...... 10 deﬁnition symbols ...... 15 dingbat (package) 39, 40, 43, 49, \curlyvee (O) ...... 17 \deg (deg) ...... 27 56, 57 \degree (0) ...... 34 \curlyvee (g) ...... 15 dingbat symbols ...... 39–44 \curlyveedownarrow ( ) . . . 16 degrees . . . . . see \textdegree \div (÷) ...... 15 \curlyveeuparrow ( )...... 16 \DEL () ...... 38 \divdot (£) ...... 17 \curlywedge (N) . ./ ...... 17 \Deleatur ..... see \Denarius \divideontimes ( ) ...... 17 delimiters ...... 29 \curlywedge (f) ...... 15 \divideontimes (>) ...... 15 \curlywedgedownarrow ( ) . 16 variable-sized ...... 30 \divides () ...... 21 \curlywedgeuparrow ( )' . . . 16 \Delta (∆) ...... 28 division times ...... see \curlyyogh (a) . . . .& ...... 10 \delta (δ) ...... 28 \divideontimes \curlyz (^) ...... 10 \deltaup (δ) ...... 28 \DJ (Ð) ...... 7 \currency ( ) ...... 13 \Denarius (¢) ...... 13 \dj () ...... 7 \dental (ag) ...... 12 ( currency symbols¤ ...... 12, 13 \dlbari ( ) ...... 10 \curvearrowbotleft (ó) . . 26 \descnode ( ) ...... 36 \DLE () ...... 38 \curvearrowbotleftright (õ) \det (det) . ...... 27 \dlsh (ê) ...... 26 ...... 26 \DH (D)...... 8 does not exist . . . see \nexists Ð \curvearrowbotright (ô) . . 26 \DH ( ) ...... 7 dollar sign ...... see \$ ( ) ...... 8 \curvearrowleft (ð) . . . . . 26 \dh \Dontwash (Ý) ...... 46 \dh (ð) ...... 7 \curvearrowleft (x) . . . . . 25 k \dot ( ˙ ) ...... 31 \curvearrowleftright (ò) . 26 diacritics ...... see accents dot symbols ...... 33 \curvearrowright (ñ) . . . . 26 diæresis ...... see accents \dotdiv (¡) ...... 17 \diagdown (å) ...... 34 \curvearrowright (y) . . . . 25 \Doteq ...... see \doteqdot \diagdown ( ) ...... 33 ( ) ...... 20 \Cutleft (s) ...... 39 \doteq \diagup (ä) ...... 34 ( ) ...... 20 \Cutline (r) ...... 39 \doteqdot + \diagup ( ) ...... 33 dotless i (ı) \Cutright (q) ...... 39 \diameter (I) ...... 34 math mode ...... 31, 33 D \diameter ( ) ...... 45 text mode ...... 10 d (esvect package option) . . . 32 \Diamond (^ ) ...... 33, 34 dotless j () \diamond () ...... 15 \d (a.) ...... 10 math mode ...... 31, 33 \dag () ...... 7 \Diamondblack (_) ...... 34 text mode ...... 10 \dagger (†) ...... 15 \Diamonddot () ...... 34 \dotplus ( ) ...... 17 \DiamonddotLeft ( ) . . . . 26 \daleth (k) ...... 29 \dotplus (u) ...... 15 dangerous bend symbols . . . 43 \Diamonddotleft () . . . . 26 \dots (. . . ) ...... 7 \dasharrow ...... see \DiamonddotRight () . . . . 26 dots (ellipses) ...... 7, 33, 51 \dashrightarrowR \Diamonddotright () . . . . 26 \dotsb (···) ...... 33 \dashint (−) ...... 51 \DiamondLeft () ...... 26 \dotsc (...) ...... 33 \Diamondleft ( ) ...... 26 \dashleftarrow (c) ...... 25 \dotseq ( ) ...... 21 \DiamondRight ( ) ...... 26 \dashleftrightarrow (e) . . 26 \dotsi (···©) ...... 33 \Diamondright ( ) ...... 26 \dashrightarrow (d) . . . . . 25 \dotsint ( ) ...... 19 diamonds ...... 42, 43 \DashV ()) ...... 21 \dotsm (···) ...... 33 diamonds (suit) . . . . . 33, 34, 44 \Dashv ()) ...... 21 \dotso (...) ...... 33 ¢ \dashv (a) ...... 20 \DiamondShadowA (¥) . . . . . 42 \dottimes ( ) ...... 17 Z \dashVv (-) ...... 21 \DiamondShadowB (¦) . . . . . 42 \doublebarwedge ( ) . . . . . 17 \doublebarwedge ( ) ...... 15 \davidsstar ( ) ...... 41 \DiamondShadowC (§) . . . . . 42 [ \doublecap ...... see \Cap \DavidStar (0C) ...... 41 6 \Diamondshape ( ) ...... 42 \doublecap (\) ...... 17 / \DavidStarSolid ( ) . . . . . 41 \DiamondSolid (p) ...... 43 \doublecup ...... see \Cup \dbar (¯d) ...... 50 \diamondsuit (♦) ...... 33 \doublecup (]) ...... 17 \dbend () ...... 43 \diatop ...... 12, 52 \DOWNarrow ( ) ...... 45 \DCa () ...... 38 \diaunder ...... 12, 52 \Downarrow (L⇓) ...... 25, 30 \DCb () ...... 38 dice ...... 47, 48 \downarrow ...... 52 \DCc (‼) ...... 38 dictionary symbols . see phonetic \downarrow (↓) ...... 25, 30 \DCd (¶) ...... 38 symbols \downbracketfill ...... 52

\ddag ( ) ...... 7 \digamma (z) ...... 28 \downdownarrows (Ó) . . . . . 26 (‡) ...... 15 \ddagger R digits ...... 34 \downdownarrows () . . . . . 25 \ddashint (=) ...... 51 circled ...... 41 \downdownharpoons (Û) . . . . 27 .... \ddddot ( ) ...... 31 LCD ...... 36 Downes, Michael J. . . . . 28, 57

61 \downharpoonleft (å) . . . . . 27 \eqslantless (¶) ...... 24 \FilledBigTriangleLeft (R) 42 \downharpoonleft () . . . . . 25 \eqslantless (0) ...... 23 \FilledBigTriangleRight (T) \downharpoonright (ç) . . . . 27 \equiv (≡) ...... 15, 20 ...... 42 ( ) . . . . 25 \er () ...... 10 \downharpoonright \FilledBigTriangleUp (Q) . 42 \downp (u) ...... 12 \ESC (←) ...... 38 (e) ...... 42 \downparenthfill ...... 52 escapable characters ...... 7 \FilledCircle ( ) ...... 46 \downt (m) ...... 12 \esh (M) ...... 10 \FilledCloud \downtouparrow (ÿ) ...... 26 esint (package) ...... 19, 56 \FilledDiamondShadowA (¨) 42 \downuparrows (×) ...... 26 \Estatically (J) ...... 38 \FilledDiamondShadowC (©) 42 \downupharpoons (ë) ...... 27 esvect (package) ...... 32, 56 \FilledDiamondshape (f) . . 42 ë \eta (η) ...... 28 \drsh ( ) ...... 26 \FilledHut () ...... 47 dsfont (package) ...... 35, 56 \etaup (η) ...... 28 \FilledRainCloud (!) . . . . 46 \dz () ...... 10 \ETB () ...... 38 ¢ \eth (ð) ...... 33 \FilledSectioningDiamond ( ) E \eth () ...... 10 ...... 47 e (esvect package option) . . . 32 \ETX (♥) ...... 38 \FilledSmallCircle (u) . . 42 e-TEX ...... 30 eufrak (package) ...... 35 \FilledSmallDiamondshape (v) e \Earth (C) ...... 37 \EUR ( ) ...... 13 ...... 42 \EURcr ( ) ...... 13 \Earth (Ê) ...... 36 d \FilledSmallSquare (p) . . 42 \earth ( ) ...... 36 \EURdig (D) ...... 13 \FilledSmallTriangleDown (s) \Ecommerce ( ) ...... 13 \EURhv (c) ...... 13 ♁ ...... 42 \EightAsterisk (Z) ...... 41 \euro ...... 13 euro signs ...... 13 \FilledSmallTriangleLeft (r) (S) . . . 41 \EightFlowerPetal eurosym (package) . . . 13, 56, 57 ...... 42 \EightFlowerPetalRemoved (Y) \EURtm (e) ...... 13 \FilledSmallTriangleRight ...... 41 euscript (package) . . . 35, 56, 57 (t) ...... 42 \eighthnote ( ) ...... 45 exclusive or ...... 48 \FilledSmallTriangleUp (q) 42 H D \EightStar ( ) ...... 41 \exists ( ) ...... 29 \FilledSnowCloud ($) . . . . 46 I \exists (∃)...... 29 \EightStarBold ( ) ...... 41 \FilledSquare (`) ...... 42 \exp (exp) ...... 27 \EightStarConvex (F) . . . . 41 \Explosionsafe ( ) ...... 38 \FilledSquareShadowA (£) . 42 E ` \EightStarTaper ( ) . . . . . 41 extensible accents 31, 32, 51–52 \FilledSquareShadowC (¤) . 42 e \ejective ( ) ...... 10 extensible arrows ...... 31, 32 \filledsquarewithdots (C) 43 electrical symbols ...... 36 extension characters ...... 27 (#) . . . . . 46 \ell (`) ...... 29 \eye (E) ...... 43 \FilledSunCloud b (c) . . 42 \Ellipse ( ) ...... 43 \EyesDollar (¦) ...... 13 \FilledTriangleDown ellipses (dots) ...... 7, 33, 51 \FilledTriangleLeft (b) . . 42 ellipses (ovals) ...... 43 F \FilledTriangleRight (d) . 42 e f (esvect package option) . . . 32 \EllipseShadow ( ) ...... 43 \FilledTriangleUp (a) . . . 42 \fallingdotseq () ...... 21 \EllipseSolid (c) ...... 43 \FilledWeakRainCloud (") . 46 \fallingdotseq ( ) ...... 20 \EM (↓) ...... 38 ; \FallingEdge (!) ...... 36 \fint ( ) ...... 19 \Email ( ) ...... 38 k \fatbslash ( ) ...... 16 \fint ( ) ...... 19 \Emailct ( ) ...... 38 z \fatsemi ( )) ...... 16 \Finv (F>) ...... 29 \emptyset (∅) ...... 33 \fatslash #( ) ...... 16 \Finv (`) ...... 29 \eng (8) ...... 10 \FAX ( ) ...... ( 38 \Fire ( )...... 47 engineering symbols . . . . 36, 38 u \fax ( ) ...... 38 R \ENQ (♣) ...... 38 t \FiveFlowerOpen ( ) . . . . . 41 \Faxmachine ( ) ...... 38 v \FiveFlowerPetal (P) . . . . 41 \Envelope ( ) ...... 44 fc (package) ...... 8, 10 8 \EOT (♦) ...... 38 fclfont (package) ...... 56 \FiveStar ( ) ...... 41 \epsilon () ...... 28 ; \FEMALE () ...... 38 \FiveStarCenterOpen ( ) . . 41 \epsilonup () ...... 28 \Female (~) ...... 38 \FiveStarConvex (?) . . . . . 41 () ...... 21 \eqbumped \female ( ) ...... 38 7 \FiveStarLines ( ) ...... 41 \eqcirc ( ) ...... 21 \FemaleFemale ( ) ...... 38 ♀ „ \FiveStarOpen (9) ...... 41 \eqcirc (P) ...... 20 \FemaleMale ( ) ...... 38 … : \Eqcolon (I) ...... 21 \FF (♀) ...... 38 \FiveStarOpenCircled ( ) . 41 \eqcolon () ...... 21 < \FHBOLOGO (f)...... 46 \FiveStarOpenDotted ( ) . . 41 \eqcolon ( ) ...... 21 E \FHBOlogo (F) ...... 46 \FiveStarOutline (=) . . . . 41 \Eqqcolon (G) ...... 21 \FilledBigCircle (U) . . . . 42 \FiveStarOutlineHeavy (>) 41 \eqqcolon (C) ...... 21 \FilledBigDiamondshape (V) 42 @ \eqsim (h) ...... 21 \FiveStarShadow ( ) . . . . . 41 \eqslantgtr (·) ...... 24 \FilledBigSquare (P) . . . . 42 \Fixedbearing (%) ...... 38 \eqslantgtr (1) ...... 23 \FilledBigTriangleDown (S) 42 \Flag () ...... 47

62 \flapr (D) ...... 10 \gemini ( ) ...... 37 \HalfCircleRight (r) . . . . . 43 \flat ([) ...... 33, 45 genealogical^ symbols ...... 45 \HalfFilledHut ( ) ...... 47 \Flatsteel (–)...... 38 \geneuro (AC) ...... 13 \halflength (p) ...... 12 ﬂowers ...... 41, 42 \geneuronarrow (BC) ...... 13 \halfnote ( ) ...... 45 C \Fog ( ) ...... 46 \geneurowide (C) ...... 13 \HalfSun ( ) ...... 46 \Gentsroom ( ) ...... 43 font encodings ...... 6 x Hamiltonian (H) see alphabets, 7-bit ...... 6 geometric shapes ...... 42, 43 math (¥) ...... 24 8-bit ...... 6 \geq \HandCuffLeft () ...... 40 ASCII ...... 56 \geq (≥) ...... 23, 24 \HandCuffLeftUp () . . . . . 40 document ...... 54 \geqq (¯) ...... 24

Latin 1 ...... 56 \geqq (=) ...... 23 \HandCuffRight ( ) ...... 40 limiting scope of ...... 6 \geqslant (>) ...... 23 \HandCuffRightUp () . . . . 40 LY1 ...... 6 \gets ...... see \leftarrow \HandLeft () ...... 40 OT1 ...... 6, 7, 10, 53 \gg (") ...... 24 \HandLeftUp () ...... 40 T1 ...... 6–8, 10, 53, 54 \gg () ...... 23 T4 ...... 8, 10 \ggcurly (Ï) ...... 21 \HandPencilLeft ( ) . . . . . 40 fontdef.dtx (ﬁle) . . . . . 48, 51 \ggg (Ï) ...... 24 \HandRight () ...... 40 fontenc (package) . . . 6–8, 10, 54 \ggg (≫ vs. Ï) ...... 49 \HandRightUp () ...... 40 \fontencoding ...... 6 \ggg (≫) ...... 23 hands ...... 40 fonts, PostScript \gggtr ...... see \ggg \Handwash (Ü)...... 46 harpoons ...... 25, 27 29 ...... (ג) Courier ...... 13 \gimel Helvetica ...... 13 \girl (B ) ...... 37 \hash (#) ...... 34 Symbol ...... 48 \glotstop (b) ...... 10 hash mark ...... see \# Times ...... 13 \gluon ( ) ...... 36 \hat (ˆ) ...... 31 Zapf Chancery ...... 35 \gnapprox (Ë) ...... 24 QPPPPPPR \HBar ()...... 42 Zapf Dingbats . . . . 39, 41 \gnapprox () ...... 23 \hbar (~) ...... 29, 50 \Football ( )...... 43 \gneq () ...... 24 o \Heart ( ) ...... 46 \forall (∀)...... 29 \gneq ( ) ...... 23 Œ hearts (suit) ...... 33, 34, 44 \Force (l) ...... 38 \gneqq (³) ...... 24 \heartsuit (♥) ...... 33 \Forward (·) ...... 46 \gneqq ( ) ...... 23 Hebrew ...... 29 \ForwardToEnd (¸) ...... 46 \gnsim (Å) ...... 24 Helvetica ...... 13 \ForwardToIndex (¹) . . . . 46 \gnsim ( ) ...... 23 \HERMAPHRODITE ( ) ...... 38 \FourAsterisk (1) ...... 41 \grave (`) ...... 31 \Hermaphrodite ( ) ...... 38 (V) . . . . . 41 greater-than sign see inequalities } \FourClowerOpen \hexagon ( ) ...... 42 Greek ...... 28, 35 \FourClowerSolid (W) . . . . 41 \Hexasteel ( ) ...... 38 \GS (↔) ...... 38 7 ’ Fourier transform (F).... see \hexstar ( ) ...... 41 \gtrapprox (Ç) ...... 24 alphabets, math \HF ( ) ...... 36 5 \gtrapprox ( ) ...... 23 A \FourStar ( ) ...... 41 ' Hilbert space ( ) see alphabets, \gtrdot (Í) ...... 24 ¬ H \FourStarOpen (6) ...... 41 math \gtrdot ( ) ...... 23 \fourth (4) ...... 34 m Holt, Alexander ...... 1, 56 \gtreqless (½) ...... 24 fraktur . . . see alphabets, math \hom (hom) ...... 27 \gtreqless ( ) ...... 23 \frown (_) ...... 20 R \hookb (¨) ...... 10 ¿ \frownie ( ) ...... 45 \gtreqqless ( ) ...... 24 \hookd () ...... 10 \Frowny (§/) ...... 46 \gtreqqless (T) ...... 23 \hookg () ...... 10 \FS (└) ...... 38 \gtrless (») ...... 24 \hookh ($) ...... 10 \FullFHBO () ...... 46 \gtrless ( ) ...... 23 \hookheng (%) ...... 10 M ≷ \fullmoon ( ) ...... 37 \gtrsim (Á) ...... 24 \hookleftarrow (←-) ...... 25 \fullmoon ( ) ...... 36 \gtrsim (&) ...... 23 \hookrevepsilon ( ) ...... 10 \fullnote (#) ...... 45 \guillemotleft () . . . . . 8, 55 \hookrightarrow (,→) . . . . . 25 \guillemotright () . . . . 8, 55 \hslash (}) ...... 29 G \guilsinglleft () ...... 8 \HT ( ) ...... 38 \G (a) ...... 10 \guilsinglright () ...... 8 Hungarian umlaut . see accents g (esvect package option) . . . 32 \gvertneqq (µ) ...... 24 \Hut () ...... 47 \Game (G) ...... 29 \gvertneqq () ...... 23 \hv (") ...... 10 \Game (a) ...... 29 \Gamma (Γ) ...... 28 H \gamma (γ) ...... 28 I \H (˝a) ...... 10 \gammaup (γ) ...... 28 \i (ı) ...... 10 h (esvect package option) . . . 32 \gcd (gcd) ...... 27 IBM ...... 38, 53 h´aˇcek ...... see accents \ge ...... see \geq \IceMountain ( ) ...... 47 \Gemini (R ) ...... 37 \Hail ()...... 46 \idotsint ( ) . . . . . 18, 19 \Gemini (â) ...... 37 \HalfCircleLeft (s) ...... 43 \iff . see \Longleftrightarrow ' 63 ifsym (package) . 36, 42, 46, 47, \JackStar (2) ...... 41 \lcm (lcm) ...... 53 49, 56, 57 \JackStarBold (3) ...... 41 \lcorners (v) ...... 29 \iiiint (§ ) ...... 18, 19 Jewish star ...... 41 \ldotp (.) ...... 33 \iiiint µ( ) ...... 19 \jmath () ...... 29, 31 \ldots (...) ...... 33 \iiint ( %) ...... 18 \Joch () ...... 47 \le ...... see \leq \leadsto ( ) ...... 20, 25 \iiint (¥ ) ...... 18, 19 \Join (Z) ...... 20 { \left ...... 30 \iiint ´( ) ...... 19 \joinrel ...... 50 \LEFTarrow ( ) ...... 45 \iint ( #) ...... 18 \Jupiter (E ) ...... 37 \Leftarrow (⇐) ...... 15, 25 \iint ( ) ...... 18, 19 \Jupiter (Å) ...... 36 £ \leftarrow (Ð) ...... 26 \iint ( ) ...... 19 \jupiter ( ) ...... 36 \leftarrow (←) ...... 25 \Im (=) ...... 29 X ! \leftarrowtail ( ) ...... 25 \imath (ı) ...... 29, 31 K \leftarrowtriangle ( ) . . 26 \impliedby see \Longleftarrow \k ( ) ...... 10 \leftbarharpoon (Ü)^ . . . . . 27 \implies see \Longrightarrow \kappa (κ) ...... 28 \LEFTCIRCLE ( ) ...... 45 \in (P) ...... 29 \kappaup (κ) ...... 28 \LEFTcircle ( ) ...... 45 \in (∈) ...... 29 \ker (ker) ...... 27 G \Leftcircle ( ) ...... 45 \Industry ( ) ...... 43 \Keyboard (Ï) ...... 37 G# I \leftharpoondown (â) . . . . 27 inequalities ...... 23, 24 Knuth, Donald E. . . . 6, 53, 57 I \leftharpoondown ()) . . . . 25 \inf (inf) ...... 27 symbols by ...... 43, 45 \leftharpoonup (à) ...... 27 \Info ( ) ...... 43 \kreuz ( ) ...... 45 i \leftharpoonup (() ...... 25 information symbols ...... 43 \Kutline6( ) ...... 39 R \leftleftarrows (Ð) . . . . . 26 \infty (8) ...... 34 \leftleftarrows ( ) . . . . . 25 \infty (∞) ...... 33 L ⇔ \leftleftharpoons (Ø) . . . 27 \injlim (inj lim) ...... 28 \L (L) ...... 7 \leftmoon (K ) ...... 37 \inplus ( ) ...... 20 \l ( l) ...... 7 ³ \leftmoon ( ) ...... 36 \int ( )A ...... 18 \labdentalnas (4) ...... 10 R \leftp (v) ...... 12 ( ) ...... 17 \Ladiesroom ( ) ...... 43 $ \int y \leftpointright (R) . . . . 40 integers (Z) see alphabets, math Lagrangian (L). see alphabets, math \Leftrightarrow (⇔) . . . . . 25 integrals ...... 17–19, 50–51 \leftrightarrow (Ø) . . . . . 26 \Lambda (Λ) ...... 28 \intercal (|) ...... 15 \leftrightarrow (↔) . . . . . 25 \lambda (λ) ...... 28 \interleave ( ) ...... 16 \leftrightarroweq ( ) . . . . 26 9 \lambdabar (o) ...... 34 intersection ...... see \cap \leftrightarrows (Ô-) . . . . 26 \lambdaslash (n) ...... 34 \Interval () ...... 47 \leftrightarrows ( ) . . . . 25 \lambdaup (λ) ...... 28 \inva ( ) ...... 10 \leftrightarrowtriangle ( ) Lamport, Leslie ...... 54, 57 \invamp (M) ...... 16 ...... 26 ] \land ...... see \wedge \invdiameter ( ) ...... 45 % \leftrightharpoon (à) . . . 27 \landdownint# ( ) ...... 19 \inve ( ) ...... 8 \leftrightharpoons (è) . . 27 \landupint ( ) ...... 19 \invf (U,) ...... 10 \leftrightharpoons ( ) . . 25 \Langle (<) ...... 35 \invglotstop (d) ...... 10 \leftrightsquigarrow (ú) 26 \langle (h) ...... 30 \invh (&) ...... 10 \leftrightsquigarrow ( ) 25 Laplace transform ( ).... see ! \invlegr (I) ...... 10 L \Leftscissors ( ) ...... 39 alphabets, math S \invm (5) ...... 10 \leftslice ( ) ...... 16 \invneg ( ) ...... 20 \leftsquigarrow2 (ø) . . . . 26 \largepencil (W) ...... 39 \invr (G) ...... 10 \leftsquigarrow (f) . . . . . 26 \invscr (K) ...... 10 \Laserbeam (a) ...... 38 \leftt (n) ...... 12 \invscripta (£) ...... 10 LATEX 1, 6, 27, 28, 30, 32, 33, 39, \leftthreetimes ($) . . . . . 34 ¤ \invv ( ) ...... 10 48, 50–52, 54, 56, 57 \leftthreetimes (h) . . . . . 15 \invw (Z) ...... 10 LATEX 2ε ...... 1,6, \leftthumbsdown (D) . . . . 40 \invy (\) ...... 10 7, 13–15, 20, 22, 25, 31, 33, \leftthumbsup (U) ...... 40 \iota (ι) ...... 28 46, 48, 49, 51, 53–55, 57 \lefttorightarrow (ü) . . . 26 \iotaup (ι) ...... 28 latexsym (package) 15, 20, 22, 25, \Lefttorque (&) ...... 38 \ipagamma ( ) ...... 10 33, 48, 56, 57 \leftturn ( ) ...... 45 / \IroningI (¯) ...... 46 \latfric ( ) ...... 10 \legm (6) ." ...... 10 \IroningII (°) ...... 46 Latin 1 ...... 6, 53, 56 \legr (E) ...... 10 \IroningIII (±) ...... 46 table ...... 55 \length (q) ...... 12 \Irritant ( ) ...... 47 laundry symbols ...... 46 \Leo (ä) ...... 37 \ismodeledby (=|) ...... 50 \Lbag (P) ...... 29 \leo ( ) ...... 37 ISO character entities . . . . . 54 \lbag (N) ...... 29 \leq (¤) ...... 24 isoent (package) ...... 54 \lbbbrack (v) ...... 30 \leq (≤) ...... 23, 24 \Lbrack ([) ...... 35 \leqq (®) ...... 24 J LCD digits ...... 36 \leqq (5) ...... 23 \j () ...... 10 \lceil (d) ...... 30 \leqslant (6) ...... 23

64 Ê less-than sign . . see inequalities \lnapprox ( ) ...... 24 \MaleMale (ƒ) ...... 38 \lessapprox (Æ) ...... 24 \lnapprox () ...... 23 \maltese (z) ...... 14 \lessapprox (/) ...... 23 \lneq (¬) ...... 24 \manboldkidney () ...... 45 \lessdot (Ì) ...... 24 \lneq ( ) ...... 23 \manconcentriccircles ($) 45 \lessdot (l) ...... 23 \lneqq (²) ...... 24 \manconcentricdiamond (%) 45 \lesseqgtr (¼) ...... 24 \lneqq () ...... 23 \mancone (#) ...... 45 \lesseqgtr (Q) ...... 23 \lnot ...... see \neg \mancube () ...... 45 Ä \lesseqqgtr (¾) ...... 24 \lnsim ( ) ...... 24 \manerrarrow (y) ...... 45 \lnsim () ...... 23 \manfilledquartercircle (!) 45 \lesseqqgtr ( ) ...... 23 S \log (log) ...... 27, 53 manfnt (package) . 43, 45, 56, 57 º \lessgtr ( ) ...... 24 log-like symbols ...... 27, 28 \manhpennib () ...... 45 \lessgtr (≶) ...... 23 logical operators \manimpossiblecube () . . . 45 À \lesssim ( ) ...... 24 and ...... see \wedge \mankidney () ...... 45 \lesssim (.) ...... 23 not ...... see \neg \manlhpenkidney () ...... 45

\Letter ( ) ...... 47 or ...... see \vee \manpenkidney () ...... 45 \Letter (B vs. ) ...... 49 \logof ( ) ...... 20 \manquadrifolium (&) . . . . 45 \Letter (B) ...... 38 \Longleftarrow (⇐=) . . . . . 25 \manquartercircle ( ) . . . . 45 letter-like symbols ...... 29 \longleftarrow (←−) . . . . . 25 letters ...... see alphabets \Longleftrightarrow . . . . . 46 \manrotatedquadrifolium (') barred ...... 50 \Longleftrightarrow (⇐⇒) 25 ...... 45 non-ASCII ...... 7 \longleftrightarrow (←→) 25 \manrotatedquartercircle (") variant Latin ...... 28 \Longmapsfrom (⇐=) ...... 26 ...... 45 \LF ( ) ...... 38 \longmapsfrom (←−)\ ...... 26 \manstar () ...... 45 7 \lfilet ( ) ...... 30 \Longmapsto (=⇒)[ ...... 26 \mantiltpennib () ...... 45 \lfloor (b) ...... 30 \longmapsto (7−→) ...... 25 \mantriangledown (7) . . . . . 45 ( ) . . . . 45 \lg (lg) .8 ...... 27 \LongPulseHigh (&) . . . . . 36 \mantriangleright x \LongPulseLow (') . . . . . 36 \mantriangleup (6) ...... 45 \lgroup (:) ...... 30 \Longrightarrow (=⇒) . . . . 25 \manvpennib () ...... 45 \LHD ( ) ...... 16 \longrightarrow (−→) . . . . 25 \Mappedfromchar () ...... 27 \lhd (C) ...... 15, 16 \looparrowdownleft (î) . . 26 \mappedfromchar () ...... 27 \lhdbend (~) ...... 43 \looparrowdownright (ï) . . 26 \Mapsfrom (⇐) ...... 26 \ \Libra (æ) ...... 37 \looparrowleft (ì) ...... 26 \mapsfrom (←) ...... 26 [ û \libra ( ) ...... 37 \looparrowleft (") ...... 25 \Mapsfromchar () ...... 27 í \Mapsfromchar () ...... 27 \Lightninga (E vs. ) . . . . . 49 \looparrowright ( ) . . . . . 26 \mapsfromchar ()ß\ ...... 27 \Lightning (E) ...... 38 \looparrowright (#) . . . . . 25 \mapsfromchar () ...... 27 \Lightning () ...... 46 \Loosebearing ($) ...... 38 (⇒) . .[ ...... 26 \lightning ( vs. ) ...... 49 \lor ...... see \vee \Mapsto o \mapsto (7→) ...... 25 \lightning ( ) . . ...... 26 \LowerDiamond ( ) ...... 42 \Mapstochar ()ú ...... 27 \lightning ( ) ...... 45 \lozenge (♦) ...... 33 \lim (lim) ...... 27, 53 \Lparen (() ...... 35 \Mapstochar () ...... 27 Þ \liminf (lim inf) ...... 27 \lrcorner ({) ...... 29 \mapstochar () ...... 27 \Mars (D ) ...... 37 \limsup (lim sup) ...... 27 \lrcorner (y) ...... 29 \Mars ( ) ...... 36 \Lineload (L) ...... 38 \lrJoin ...... see \Join Ä linguistic symbols ...... 8–10 \lrtimes (\) ...... 21 \mars ( ) ...... 36 \MartinVogel ( ) ...... 46 \lJoin (X) ...... 21 \Lsh (è) ...... 26 ♂ ÿ marvosym (package) . . . . 13, 34, \ll (!) ...... 24 \Lsh () ...... 25 36–39, 43, 46, 49, 56, 57 \ll () ...... 23 \Lsteel (™) ...... 38 \llap ...... 51 \ltimes ( ) ...... 17 matbbol (package) ...... 35 \llbracket (~) ...... 30 \ltimes (n) ...... 15 math alphabets ...... 35 \llceil ( )...... 29 \lvertneqq (´) ...... 24 mathabx (package) . . . . . 17, 18, \llcornerV(z) ...... 29 \lvertneqq () ...... 23 20–24, 26, 27, 29–32, 34, 37, 1 43, 48, 49, 56, 58 \llcorner (x) ...... 29 \lz ( ) ...... 10 \llcurly (Î) ...... 21 \mathbb ...... 35 \mathbbm ...... 35 \Lleftarrow (W) ...... 25 M \llfloor ( ) ...... 29 \M ...... 8 \mathbbmss ...... 35 \lll (Î) .T ...... 24 \m ...... 8 \mathbbmtt ...... 35 mathbbol (package) ...... 35 \lll (≪ vs. Î) ...... 49 macron ...... see accents \mathbin ...... 52 \lll (≪) ...... 23 majuscules ...... 28 \llless ...... see \lll \makeatletter ...... 51 mathcal (euscript package option) \llparenthesis8 ( ) ...... 29 \makeatother ...... 51 ...... 35 L \MALE ( ) ...... 38 \mathcal ...... 35 \lmoustache (;) ...... 30 ‚ \Male (|) ...... 38 \mathcent (¢) ...... 29 \ln (ln) ...... 27 \male ( ) ...... 38 \mathchoice ...... 50 ♂ 65 \mathclose ...... 52 \multimapdotboth () . . . . 21 \newmoon ( ) ...... 36 mathcomp (package) . . . 34, 56 \multimapdotbothA () . . . 21 \newtie (a) ...... 10 \mathds ...... 35 \multimapdotbothAvert () . 21 \nexists (E) ...... 29 mathematical symbols . . 15–35 \multimapdotbothB () . . . 21 \nexists (@) ...... 29 \mathfrak ...... 35 \multimapdotbothBvert () . 21 \NG ()...... 7 \mathit ...... 35 \multimapdotbothvert () . . 21 \ng () ...... 7 \mathnormal ...... 35 \multimapdotinv () . . . . . 21 \ngeq (§) ...... 24 \mathop ...... 52 \multimapinv () ...... 21 \ngeq () ...... 23, 24 \mathopen ...... 52 multiple accents per character 52 \ngeqq (±) ...... 24 ( ) ...... 46 \mathord ...... 52 \Mundus m \ngeqq () ...... 23 \mathpunct ...... 52 musical notes ...... 14, 33, 45 \ngeqslant ( ) ...... 23 \muup (µ) ...... 28 \mathpzc ...... 35 \ngg (4) ...... 24 \MVAt ( ) ...... 46 \mathrel ...... 50, 52 @ \ngtr (£) ...... 24 \mathring (˚) ...... 31 \MVEight ( ) ...... 34 8 \ngtr (≯) ...... 23 \MVFive ( ) ...... 34 \mathrm ...... 35 5 \ngtrapprox (É) ...... 24 \MVFour ( ) ...... 34 mathrsfs (package) . . . . . 35, 56 4 \ngtrapprox (#) ...... 24 \MVNine ( ) ...... 34 mathscr (euscript package option) 9 \ngtrless (&) ...... 24 \MVOne ( ) ...... 34 ...... 35 1 \ngtrsim (Ã) ...... 24 \MVSeven ( ) ...... 34 \mathscr ...... 35 7 \ngtrsim (!) ...... 24 \MVSix ( ) ...... 34 \mathsterling (£) ...... 29 6 \ni (3) ...... 29 \MVThree ( ) ...... 34 \max (max) ...... 27 3 \nialpha (¢) ...... 10 \MVTwo ( ) ...... 34 \maya ...... 34 2 \nibar ...... see \ownsbar \MVZero ( ) ...... 34 \mbox ...... 51 0 \nibeta (©) ...... 10 \measuredangle (>) ...... 34 N \NibLeft () ...... 40 \measuredangle (]) ...... 33 \nabla (∇) ...... 33 \NibRight () ...... 40 \medbullet () ...... 16 \NAK (§) ...... 38 nibs ...... 40 \medcirc () ...... 16 () ...... 22 \Mercury (A ) ...... 37 \napprox \NibSolidLeft ( ) ...... 40 \napproxeq ( ) ...... 21 \Mercury ( ) ...... 36 6 \NibSolidRight ( ) ...... 40 Â \nasymp ( ) ...... 21 \mercury ( ) ...... 36 - \nichi ([) ...... 10 \natural (\) ...... 33, 45 \merge ( ) ...... 16 \niepsilon () ...... 10 ' natural numbers (N)..... see METAFONT! book symbols . . . 45 \nigamma ( ) ...... 10 alphabets, math \mho ( ) ...... 33, 34 \niiota ()) ...... 10 f navigation symbols ...... 46 Microsoft Windows ...... 54 \nilambda (2) ...... 10 \nbacksim ( ) ...... 21 \mid (|) ...... 20 * \niomega (>) ...... 10 \nbacksimeq ( ) ...... 21 \middle ...... 30 + \niphi (C) ...... 10 \nBumpeq ()) ...... 21 \midtilde ({) ...... 12 \niplus ( ) ...... 20 \nbumpeq (() ...... 21 \min (min) ...... 27, 53 \nisigma B(O) ...... 10 \ncong () ...... 22 \minuso ( ) ...... 16 \nitheta (S) ...... 10 \ncong ( ) ...... 20 miscellaneous symbols . . 33, 34, \niupsilon (V) ...... 10 \ncurlyeqprec (¸) ...... 22 43–47 \nj (7) ...... 10 \ncurlyeqsucc (¹) ...... 22 “Missing $ inserted” . . . . 15 \nLeftarrow (ö) ...... 26 \nDashV (+) ...... 22 \Mmappedfromchar () ...... 27 \nLeftarrow ( ) ...... 25 \nDashv (+) ...... 22 : \mmappedfromchar () ...... 27 \nleftarrow (Ú) ...... 26 \ndashV (/) ...... 22 \Mmapstochar () ...... 27 \nleftarrow ( ) ...... 25 \ndashv (') ...... 22 8 () ...... 27 \nLeftrightarrow (ø) . . . . 26 \mmapstochar \ndashVv (/) ...... 22 \nLeftrightarrow ( ) . . . . 25 \Mobilefone (H) ...... 38 \ne ...... see \neq < \nleftrightarrow (Ü) . . . . 26 \mod ...... 28 \Nearrow (t) ...... 26 \nleftrightarrow ( ) . 15, 25 \models (|=) ...... 20, 48, 50 \nearrow (Õ) ...... 26 = \nleq (¦) ...... 24 \moo ( ) ...... 16 \nearrow (%) ...... 25 ( ) ...... 23, 24 \Moon (K ) ...... 37 \neg (¬) ...... 33 \nleq \nleqq (°) ...... 24 \Moon (Á) ...... 36 \Neptune (H ) ...... 37 \nleqq ( ) ...... 23 \Mountain ( ) ...... 47 \Neptune (È) ...... 36 mouse . . . . see \ComputerMouse \neptune ( )...... 36 \nleqslant ( ) ...... 23 ¢ \MoveDown (») ...... 46 \neq () .[ ...... 22 \nless ( ) ...... 24 \MoveUp (º) ...... 46 \neq (,) ...... 23 \nless (≮) ...... 23 \mp (∓) ...... 15 \neqslantgtr (¹) ...... 24 \nlessapprox (È) ...... 24 \mu (µ) ...... 28 \neqslantless (¸) ...... 24 \nlessapprox (") ...... 24 \multimap (() ...... 20, 21 \nequiv (.) ...... 21 \nlessgtr (') ...... 24 \multimapboth () ...... 21 \neswarrow (%.) ...... 51 \nlesssim (Â) ...... 24 \multimapbothvert () . . . . 21 \Neutral ({) ...... 38 \nlesssim ( ) ...... 24 \multimapdot () ...... 21 \newmoon (N ) ...... 37 \nll (3) ...... 24

66 \nmid (-) ...... 20 \nsubset () ...... 23 o (o) ...... 28 \nnearrow ( ) ...... 26 \nsubseteq () ...... 23 \oasterisk (f) ...... 17 \nnwarrow (1) ...... 26 \nsubseteq (*) ...... 22 \obackslash (n) ...... 17 0 \NoBleech (Ì) ...... 46 \nsubseteqq ( ) ...... 23 \obar ( ) ...... 16 : \NoChemicalCleaning (¨) . . 46 \nsubseteqq (") ...... 23 \oblong ( ) ...... 16 £ k @ \NoIroning (²) ...... 46 \nsucc ( ) ...... 22 \obot ( ) ...... 17 \NoSun () ...... 46 \nsucc () ...... 20 \obslash ( ) ...... 16 É e ; not ...... see \neg \nsuccapprox ( ) ...... 22 \ocirc ( ) ...... 17 \not ...... 22 \nsuccapprox (8) ...... 21 \ocircle ( ) ...... 16 § g not equal (= vs. =) ...... 22 \nsucccurlyeq ( ) ...... 22 \ocoasterisk# ( ) ...... 17 \notasymp () ...... 22 \nsucccurlyeq (%) ...... 21 \octagon ( ) ...... 42 « \notbackslash ( \−) ...... 37 \nsucceq ( ) ...... 22 \Octosteel8(‘) ...... 38 c \notbot (M) ...... 29 \nsucceq () ...... 20 \odiv ( ) ...... 17 d \notdivides ( ) ...... 22 \nsucceqq (:) ...... 21 \odot ( ) ...... 17 Ã \notequiv () ...... 22 \nsuccsim ( ) ...... 22 \odot ( ) ...... 15 ( ) ...... 21 ¨ \notin (R) ...... 29 \nsuccsim \odplus ( ) ...... 17 \nSupset () ...... 23 \OE (Œ) ...... 7 \notin (<) ...... 29 \nSupset (?) ...... 23 \oe (œ) ...... 7 \notni (=) ...... 29 \nsupset () ...... 23 e \notowner (S) ...... 29 \officialeuro ( ) ...... 13 \nsupseteq () ...... 23 \notowns .. see \notowner and ogonek ...... see accents \nsupseteq ( ) ...... 22 \notni + \ogreaterthan ( ) ...... 16 \nsupseteqq () ...... 23 = \notperp (M) ...... 22 \oiiint ( ) ...... 19 \nsupseteqq ( ) ...... 22 \notslash (−/ ) ...... 37 # \oiiintclockwise ( ) . . . . 19 \nthickapprox ( ) ...... 21 \nottop (L) ...... 29 5 \oiiintctrclockwise) ( ) . 19 \ntriangleleft () ...... 24 · \NoTumbler ( ) ...... 46 \oiint ( ) ...... L ...... 18 \ntriangleleft ( ) ...... 24 \nparallel ( ) ...... 20 6 ∦ \ntrianglelefteq () . . . . 24 \oiint ( ) ...... D . . 18, 19 \nplus (`) ...... 16 \ntrianglelefteq ( ) . . . . 24 \oiint ( ) ...... 19 \nprec (¢) ...... 22 5 \ntrianglelefteqslant ( ) 24 \oiintclockwise ( ) . . . . . 19 \nprec ( ) ...... 20 ⊀ \ntriangleright () . .R . . . 24 \oiintctrclockwise ( ) . . 19 \nprecapprox (È) ...... 22 ¶ \ntriangleright ( ) . . . . . 24 \oint ( ) ...... H 18 \nprecapprox ( ) ...... 21 7 H 7 \ntrianglerighteq () . . . . 24 \npreccurlyeq (¦) ...... 22 \oint ( ) ...... @ ...... 17 \ntrianglerighteq (4) . . . . 24 \npreccurlyeq ( ) ...... 21 \ointclockwise ( ) ...... 19 $ \ntrianglerighteqslant ( ) 24 \npreceq (ª) ...... 22 \ointclockwise ( ) ...... 19 \ntwoheadleftarrow (h) .S . . 21 \npreceq ( ) ...... 20 \ointctrclockwise ( ) . . . . 19 \ntwoheadrightarrow (g) . . 21 ( ) ...... 21 \npreceqq 9 \nu (ν) ...... 28 \ointctrclockwise ( ) . . . . 19 Â \nprecsim ( ) ...... 22 null set ...... 33, 34 old-style digits ...... 13 \nprecsim () ...... 21 number sets see alphabets, math \oldstylenums ...... 13 ÷ h \nRightarrow ( ) ...... 26 numbers ...... see digits \oleft ( ) ...... 17 \nRightarrow (;) ...... 25 numerals ...... see digits \olessthan ( ) ...... 16 Û < \nrightarrow ( ) ...... 26 \nuup (ν) ...... 28 \Omega (Ω) ...... 28 \nrightarrow (9) ...... 25 \nvargeq («) ...... 24 \omega (ω) ...... 28 \nshortmid (.) ...... 20 \nvarleq (ª) ...... 24 \omegaup (ω) ...... 28 \ominus (a) ...... 17 \nshortparallel (/) ...... 20 \nvarparallel ( ) ...... 21 \nsim ( ) ...... 22 \nvarparallelinv ( ) . . . . . 21 \ominus ( ) ...... 15 @ \nsim (/) ...... 20 \nVDash (*) ...... 22 \oo ( ) ...... 10 \nsimeq () ...... 22 \open (z) ...... 12 \nVDash (3) ...... 20 \nsimeq (;) ...... 21 \nVdash (.) ...... 22 \openJoin ([) ...... 21 () ...... 23 \openo (=) ...... 10 \nsqSubset \nVdash (1) ...... 21 \nsqsubset () ...... 23 \nvDash (*) ...... 22 \openo ( ) ...... 8 \opentimes ( ) ...... 21 \nsqsubset (a) ...... 23 \nvDash (2) ...... 20 l ] \nsqsubseteq () ...... 23 \nvdash (&) ...... 22 operators binary ...... 15–17 \nsqsubseteq (@) ...... 23 \nvdash (0) ...... 20 \nsqsubseteqq () ...... 23 \nVvash (.) ...... 22 logical see logical operators set . . . . . see set operators \nsqSupset ( ) ...... 23 \Nwarrow (v) ...... 26 ` \nsqsupset () ...... 23 \nwarrow (Ô) ...... 26 \oplus ( ) ...... 17 \nsqsupset (b) ...... 23 \nwarrow (-) ...... 25 \oplus (⊕) ...... 15, 48 \nsqsupseteq () ...... 23 \nwsearrow (-&) ...... 51 \opposition ( ) ...... 37 \nsqsupseteq (A) ...... 23 options . . . Wsee package options \nsqsupseteqq () ...... 23 O or ...... see \vee \nSubset () ...... 23 \O (Ø) ...... 7 \oright (i) ...... 17 \nSubset (>) ...... 23 \o (ø) ...... 7 \OrnamentDiamondSolid (q) 44

67 \oslash (m) ...... 17 esvect ...... 32, 56 \PencilRightUp () ...... 40 \oslash ( ) ...... 15 eufrak ...... 35 pencils ...... 39, 40 \otimes (b) ...... 17 eurosym ...... 13, 56, 57 \pentagon ( ) ...... 42 \otimes (⊗) ...... 15 euscript ...... 35, 56, 57 percent signD ...... see \% \otop (j) ...... 17 fclfont ...... 56 \permil ( ) ...... 14 \otriangleup (o) ...... 17 fc ...... 8, 10 \Perp (y)h ...... 21 ovals ...... 43 fontenc ...... 6–8, 10, 54 \perp (⊥) ...... 20 \ovee ( ) . .hkkikkj ...... 16 ifsym 36, 42, 46, 47, 49, 56, \Pfund (£) ...... 13 > \overbrace ( ) ...... 32 57 pharmaceutical prescription see z}|{ isoent ...... 54 \textrecipe \overbrace ( ) ...... 31 latexsym . 15, 20, 22, 25, 33, \Phi (Φ) ...... 28 \overbracket ...... 51, 52 48, 56, 57 \phi (φ) ...... 28 φ \overbrackethkkkkj( ) ...... 52 manfnt . . . . . 43, 45, 56, 57 \phiup ( ) ...... 28 \overgroup ( ) ...... 32 marvosym 13, 34, 36–39, 43, \Phone (¨) ...... 44 ←− \overleftarrow ( ) ...... 31 46, 49, 56, 57 \phone ( ) ...... 45 ←→ \overleftrightarrow ( ) . 32 matbbol ...... 35 \PhoneHandset (©) ...... 44 \overline ( ) ...... 31 mathabx ...... 17, 18, phonetic symbols ...... 8–10 \overparenthesis . . . . . 51, 52 20–24, 26, 27, 29–32, 34, 37, \photon ( ) ...... 36 z{ 43, 48, 49, 56, 58 physical symbols ...... 36 \overparenthesis ( ) . . . . 52 ¬¬¬¬ −→ mathbbol ...... 35 (Π) ...... 28 \overrightarrow ( ) . . . . . 31 \Pi mathcomp ...... 34, 56 (π) ...... 28 \overring (x) ...... 12 \pi mathrsfs ...... 35, 56 ( ) ...... 38 \ovoid (l) ...... 17 \Pickup A pifont . 8, 39–44, 48, 56, 57 pifont (package) 8, 39–44, 48, 56, \owedge ( ) ...... 16 psnfss ...... 41 ? 57 \owns ...... see \ni pxfonts 15, 16, 19–29, 33–35, Q pilcrow ...... see \P \owns ( ) ...... 29 48 \ownsbar (W) ...... 29 \Pisces (ë) ...... 37 skull ...... 43, 56, 57 \pisces ( ) ...... 37 stmaryrd . 16, 18, 20, 22, 24, \Pisymbolf...... 48 P 26, 27, 29, 30, 49, 56, 57 ¶ \pitchfork (&) ...... 34 \P ( ) ...... 7, 55 textcomp 6, 7, 10, 12–14, 25, \pitchfork (t) ...... 20 \p@ ...... 51 31, 34, 36, 45, 48, 54, 56, 57 package options \piup (π) ...... 28 tipa . . . 8, 9, 11, 12, 56, 57 a (esvect) ...... 32 \Plane ( ) ...... 44 txfonts 15, 16, 19–29, 33–35, bbgreekl (mathbbol) . . . 35 playing cards . . . . see card suits 48, 50, 56, 57 b (esvect) ...... 32 ' ulsy ...... 17, 27, 56 \Plus ( )...... 40 c (esvect) ...... 32 upquote ...... 53 plus-or-minus sign . . . . see \pm d (esvect) ...... 32 url ...... 53 \PlusCenterOpen (() . . . . . 40 e (esvect) ...... 32 wasysym . . 8, 13–16, 18, 20, \pluscirc (©) ...... 17 f (esvect) ...... 32 22, 23, 25, 33, 34, 36–38, 41, & g (esvect) ...... 32 \PlusOutline ( ) ...... 40 42, 45, 49, 56, 57 h (esvect) ...... 32 plusses ...... 40 wsuipa . . 10, 12, 49, 52, 56 mathcal (euscript) . . . . . 35 \PlusThinCenterOpen ()) . . 40 yfonts ...... 35, 56, 57 mathscr (euscript) . . . . . 35 \Pluto (I) ...... 37 yhmath . . . . 31, 33, 51, 56 sans (dsfont) ...... 35 \Pluto (É) ...... 36 zapfchan ...... 56 varg (txfonts/pxfonts) . . 28 \pluto ( ) ...... 36 Pakin, Scott ...... 1, 56 packages \pm (±)\ ...... 15 \PaperLandscape (¤) . . . . . 47 accents ...... 52, 56, 57 \pmod ...... 27 amsfonts 15, 20, 22, 25, 33, \PaperPortrait (£) ...... 47 \pod ...... 28 35 paragraph mark ...... see \P \pointer ( ) ...... 45 amsmath ...... 6, 28, 52 \parallel (k) ...... 20 \Pointinghand (Z) ...... 43 amssymb . 6, 15, 20, 22, 25, \ParallelPort (Ñ) ...... 37 \polishhook (~) ...... 12 33, 35, 56–58 \partial (B) ...... 29 polygons ...... 42 amstext ...... 51 \partial (∂) ...... 29 PostScript fonts 13, 35, 39, 41, 48 ar ...... 36, 56 \partialslash (C) ...... 29 \pounds (£) ...... 7, 55 ascii ...... 38, 53, 56 parts per thousand ...... see power set (P).. see alphabets, bbding 39–41, 43, 44, 49, 56, \textperthousand math 57 \Peace () ...... 44 \Pr (Pr) ...... 27 bbm ...... 35, 56 \PencilLeft () ...... 40 \prec (≺) ...... 20 Æ bbold ...... 35, 56 \PencilLeftDown () . . . . . 40 \precapprox ( ) ...... 21 braket ...... 30 \precapprox (w) ...... 20 \PencilLeftUp () ...... 40 dingbat 39, 40, 43, 49, 56, 57 \preccurlyeq (¤) ...... 21 \PencilRight () ...... 40 dsfont ...... 35, 56 \preccurlyeq (4) ...... 20 esint ...... 19, 56 \PencilRightDown () . . . . 40 \precdot (Ì) ...... 21

68 \preceq () ...... 20 \Rectangle (u) ...... 43 \rightmoon (L ) ...... 37 \preceqq () ...... 21 \RectangleBold (v) ...... 43 \rightmoon ( ) ...... 36 \precnapprox (Ê) ...... 22 rectangles ...... 43 \rightp (w) .% ...... 12 ( ) ...... 20 (L) . . . . 40 \precnapprox \RectangleThin (t) ...... 43 \rightpointleft \precneq (¬) ...... 22 \Rectpipe ( ) ...... 38 \rightpointright (N) . . . 40 \precneqq ( ) ...... 21 ˜ \Rectsteel ( ) ...... 38 \rightrightarrows (Ñ) . . . 26 \precnsim (Ä) ...... 22 ” registered trademark . . . . . see \rightrightarrows ( ) . . . 25 \precnsim ( ) ...... 20 ⇒ \textregistered \rightrightharpoons (Ù) . . 27 \precsim (À) ...... 21 relational symbols ...... 20 \Rightscissors ( ) ...... 39 \precsim ( ) ...... 20 Q - binary ...... 20–24 \rightslice ( ) ...... 16 prescription . . see \textrecipe negated binary . . . . 20–22 \rightsquigarrow3 (ù) . . . 26 \prime (0) ...... 33 triangle ...... 24 \rightsquigarrow ( ) . . . . 25 \Printer ( ) ...... 37 Q Ò \Relbar (=) ...... 27, 50 \rightt (o) ...... 12 \prod ( ) ...... 17 \relbar (−) ...... 27, 50 \rightthreetimes (%) . . . . 34 \projlim (proj lim) ...... 28 \restoresymbol ...... 48 \rightthreetimes ( ) . . . . 15 pronunciation symbols . . . . see i \restriction ...... see \rightthumbsdown (d) . . . 40 phonetic symbols \upharpoonright \rightthumbsup (u) . . . . . 40 \propto (9) ...... 34 \restriction (æ) ...... 26 \righttoleftarrow (ý) . . . 26 \propto (∝) ...... 20 . \revddots (.. ) ...... 51 \Righttorque ( ) ...... 38 \ProvidesPackage ...... 56 ' \reve () ...... 10 \rightturn ( ) ...... 45 \Psi (Ψ) ...... 28 \reveject (f) ...... 10 \ring (˚) ...... 31 \psi (ψ) ...... 28 ! \revepsilon () ...... 10 ring equal to . . . . . see \circeq \psiup (ψ) ...... 28 reverse solidus ...... see ring in equal to . . . see \eqcirc psnfss (package) ...... 41 \textbackslash \rip (O) ...... 43 pulse diagram symbols . . . . . 36 \reversedvideodbend () . 43 \risingdotseq () ...... 21 \PulseHigh ($) ...... 36 \revglotstop (c) ...... 10 \risingdotseq ( ) ...... 20 \PulseLow (%) ...... 36 : \Rewind ( ) ...... 46 \rJoin (Y) ...... 21 punctuation ...... 8 ¶ \RewindToIndex ( ) . . . . . 46 \rlap ...... 42, 51 pxfonts (package) . 15, 16, 19–29, ´ 9 \RewindToStart ( ) ...... 46 : 33–35, 48 µ \rmoustache ( ) ...... 30 \rfilet (?) ...... 30 roots ...... see \sqrt Q \rfloor (9c) ...... 30 \RoundedLsteel (Ÿ) ...... 38 \quarternote ( ) ...... 45 ; \rgroup ( ) ...... 30 \RoundedTsteel () ...... 38 quaternions (H) see alphabets, ♩ \RHD ( ) ...... 16 \RoundedTTsteel () ...... 38 math ) \rhd ( ) ...... 15, 16 \Rparen ( ) ...... 35 \quotedblbase () ...... 8 B \rho (ρ) ...... 28 \rrbracket () ...... 30 \quotesinglbase ( ) ...... 8 \rhoup (ρ) ...... 28 \rrceil ( ) ...... 29 W \right ...... 30 \rrfloor ( ) ...... 29 R U \RIGHTarrow ( ) ...... 45 \Rrightarrow (V) ...... 26 \r (˚a) ...... 10 ( ) ...... 29 \Rightarrow . ...... 46 \rrparenthesis \Radiation () ...... 47 \RS () ...... M ...... 38 \Rightarrow (⇒ vs. : vs. ñ) 49 radicals . . see \sqrt and \surd \Rightarrow (⇒) . . . . . 15, 25 \Rsh (é) ...... 26 \Radioactivity ( ) ...... 38 \Rsh ( ) ...... 25 j \Rightarrow (:) ...... 46 \Rain ()...... 46 \rightarrow (Ñ) ...... 26 \rtimes ( ) ...... 17 \RainCloud () ...... 46 \rightarrow (→) ...... 25 \rtimes (o) ...... 15 \RaisingEdge ( ) ...... 36 \rightarrowtail () . . . . . 25 \Rangle (>) ...... 35 \rightarrowtriangle ( ) . . 26 S § \rangle (i) ...... 30 \rightbarharpoon (Ý)_ . . . . 27 \S ( ) ...... 7, 55 rational numbers (Q)..... see \RIGHTCIRCLE ( ) ...... 45 safety-related symbols . . . . . 38 ( ) ...... 37 alphabets, math \RIGHTcircle (H) ...... 45 \Sagittarius è ( ) ...... 37 rationalized Planck constant see \Rightcircle (H#) ...... 45 \sagittarius sans (dsfont package option) . 35 \hbar \RightDiamond J(?) ...... 42 c \Rbag (Q) ...... 29 \rightharpoondown (ã) . . . 27 \satellitedish (I) ...... 43 \rbag (O) ...... 29 \rightharpoondown (+) . . . 25 \Saturn (F ) ...... 37 w \rbbbrack ( ) ...... 30 \rightharpoonup (á) . . . . . 27 \Saturn (Æ) ...... 36 \Rbrack (]) ...... 35 \rightharpoonup (*) . . . . . 25 \saturn ( ) ...... 36 \rceil (e) ...... 30 \rightleftarrows (Õ) . . . . 26 \savesymbolY ...... 48 \rcorners (w) ...... 29 \rightleftarrows () . . . . 25 \Sborder (S) ...... 43 \Re (<) ...... 29 \rightleftharpoon (á) . . . 27 \scd () ...... 10 real numbers (R) see alphabets, \rightleftharpoons (é) . . 27 \scg () ...... 10 math \rightleftharpoons ( ) . . 25 \schwa () ...... 10 \recorder ( ) ...... 45 \rightleftharpoons ()*) . . 25 \sci (*) ...... 10 69 scientiﬁc symbols ...... 36–38 \simeq (') ...... 20 “special” characters ...... 7 \ScissorHollowLeft (§) . . 39 \sin (sin) ...... 27 \SpecialForty (Ú) ...... 46 \sinh (sinh) ...... 27 \sphericalangle (?) . . . . . 34 \ScissorHollowRight (¦) . 39 \SixFlowerAlternate (O) . . 41 \sphericalangle (^) . . . . . 33 \ScissorLeft (¤) ...... 39 \SixFlowerAltPetal (U) . . 41 \SpinDown ()* ...... 42 \ScissorLeftBrokenBottom (£) () ...... 42 ...... 39 \SixFlowerOpenCenter (M) . 41 \SpinUp \splitvert ...... 38 ¥ \SixFlowerPetalDotted (Q) 41 \ScissorLeftBrokenTop ( ) 39 \splitvert (¦) ...... 38 L \ScissorRight (¡) ...... 39 \SixFlowerPetalRemoved ( ) 41 \sqbullet ( ) ...... 17 \ScissorRightBrokenBottom \SixFlowerRemovedOpenPetal \sqcap ([) ...... 17 [ ( ) ...... 39 ( ) ...... 41 \sqcap (u) ...... 15 \ScissorRightBrokenTop (¢) 39 \SixStar (G) ...... 41 \sqcapplus (}) ...... 16 scissors ...... 39 \SixteenStarLight (K) . . . 41 \sqcup (\) ...... 17 \scn (:) ...... 10 skull (package) ...... 43, 56, 57 \sqcup (t) ...... 15 \Scorpio (ç) ...... 37 \skull (A) ...... 43 \sqcupplus (|) ...... 16 ^ \scorpio ( ) ...... 37 \slashb (§)...... 10 \sqdoublecap ( ) ...... 17 _ \scr (J) .b ...... 10 \slashc ( ) ...... 10 \sqdoublecup ( ) ...... 17 script letters see alphabets, math \slashd ()...... 10 \sqiiint ( ) ...... 19 ¡ \scripta ( ) ...... 10 \slashu (U)...... 10 \sqiint ( ) ...... 19 () ...... 10 \scriptg \Sleet () ...... 46 \sqiint ( R) ...... 19 \scriptv (Y) ...... 10 (E) ...... 42 \sqint (P) ...... 19 \scu (W) ...... 10 \SmallCircle \sqint ( ) ...... 19 \scy (]) ...... 10 \SmallCross () ...... 42 √ \sqrt ( ) ...... 31 \Searrow ( ) ...... 26 F u \SmallDiamondshape ( ) . . 42 \sqSubset () ...... 23 \searrow (×) ...... 26 \smallfrown (a) ...... 20 \sqsubset () ...... 23 \searrow (&) ...... 25 \SmallHBar () ...... 42 \sqsubset ( ) ...... 22 \sec (sec) ...... 27 @ \SmallLowerDiamond () . . 42 \sqsubseteq () ...... 23 \second (2) ...... 34 \smallpencil (P) ...... 39 \sqsubseteq (v) ...... 22 \secstress (i) ...... 12 O \sqsubseteqq () ...... 23 section mark ...... see \S \SmallRightDiamond ( ) . . 42 \sqsubsetneq () ...... 23 \smallsetminus (r) ...... 15 \SectioningDiamond (¡) . . 47 \sqsubsetneqq () ...... 23 \smallsmile (`) ...... 20 segmented digits ...... 36 \sqSupset () ...... 23 \SmallSquare (@) ...... 42 \selectfont ...... 6 \sqsupset () ...... 23 C semidirect products . . 15, 17, 34 \SmallTriangleDown ( ) . . 42 \sqsupset ( ) ...... 22 A \SerialInterface (Î) . . . . 37 \smalltriangledown ( ) . . . 17 \sqsupseteq ( ) ...... 23 \SerialPort (Ð) ...... 37 \SmallTriangleLeft (B) . . 42 \sqsupseteq (w) ...... 22 set operators \smalltriangleleft () . . . 17 \sqsupseteqq () ...... 23 intersection . . . . see \cap \SmallTriangleRight (D) . . 42 \sqsupsetneq () ...... 23 union ...... see \cup \smalltriangleright () . . 17 \sqsupsetneqq () ...... 23 \setminus (\) ...... 15 \SmallTriangleUp (A) . . . . 42 \Square (0) ...... 42 SGML ...... 54 \smalltriangleup () . . . . . 17 ( vs. f vs. 0) . . . 49 \sharp (]) ...... 33, 45 \Square \SmallVBar ( ) ...... 42 \Square () ...... 41 \Shilling (¡) ...... 13 \shortdownarrow ( ) ...... 26 \smile (^) ...... 20 \Square (f) ...... 43 \Smiley ( ) ...... 46 \square (¥) ...... 17 \ShortFifty (×) ...... 46 © \smiley ( ) ...... 45 \square ( ) ...... 33 \ShortForty (Ù) ...... 46 \shortleftarrow ( ) . . . . . 26 smiley faces, . . . . . see \Smiley, square root ...... see \sqrt \smiley, \SOH, and \STX \shortmid (p) . . . ...... 20 \SquareCastShadowBottomRight \Snow () ...... 46 k \ShortNinetyFive (Ô) . . . . 46 ( ) ...... 43 \shortparallel (q) ...... 20 \SnowCloud ( ) ...... 46 \SquareCastShadowTopLeft (m) \ShortPulseHigh (") . . . . . 36 \Snowflake (`) ...... 41 ...... 43 # \ShortPulseLow ( ) ...... 36 \SnowflakeChevron (^) . . . 41 \SquareCastShadowTopRight \shortrightarrow ( ) . . . . 26 (l) ...... 43 \SnowflakeChevronBold (_) 41 \ShortSixty ( ) . ...... 46 Ö snowﬂakes ...... 41, 42 \Squaredot (÷) ...... 34 \ShortThirty ( ) ...... 46 ( ) ...... 38 Û \SO (♫) ...... 38 \Squarepipe — \shortuparrow ( ) ...... 26 squares ...... 42, 43 \SOH () ...... 38 \showclock . . . ...... 47 spades (suit) ...... 33, 34, 44 \SquareShadowA ( ) ...... 42 \SI () ...... 38 \spadesuit (♠) ...... 33 \SquareShadowB (¡) ...... 42 \Sigma (Σ) ...... 28 \sigma (σ) ...... 28 \Sparkle (]) ...... 41 \SquareShadowBottomRight (h) \sigmaup (σ) ...... 28 \SparkleBold (\) ...... 41 ...... 43 \sim (∼) ...... 20, 53 sparkles ...... 41, 42 \SquareShadowC (¢) ...... 42

70 \SquareShadowTopLeft (j) . 43 \succneqq () ...... 21 genealogical ...... 45 \SquareShadowTopRight (i) 43 \succnsim (Å) ...... 22 general ...... 45 ( ) ...... 20 information ...... 43 \SquareSolid (g) ...... 43 \succnsim (Á) ...... 21 Knuth’s ...... 43, 45 \Squaresteel ( ) ...... 38 \succsim “ \succsim ( ) ...... 20 laundry ...... 46 B P % \squarewithdots ( ) . . . . . 43 \sum ( ) ...... 17 letter-like ...... 29 \squplus (]) ...... 17 \Summit () ...... 47 linguistic ...... 8–10 \SS (SS) ...... 7 log-like ...... 27, 28 \SummitSign () ...... 47 \ss (ß) ...... 7 mathematical . . . . . 15–35 \Sun (@) ...... 37 \ssearrow ( ) ...... 26 METAFONTbook . . . . . 45 @ \sslash ( )% ...... 16 \Sun (À vs. vs. ) . . . . . 49 miscellaneous 33, 34, 43–47 \sswarrow ( ) ...... 26 \Sun (À) ...... 36 navigation ...... 46 \stackrel .$ ...... 15 \Sun () ...... 46 phonetic ...... 8–10 \star (?) ...... 15, 52 \sun ( ) ...... 45 physical ...... 36 Star of David ...... 41 \SunCloud☼ () ...... 46 pulse diagram ...... 36 stars ...... 33, 41, 42 relational ...... 20 \SunshineOpenCircled (T) . 44 stmaryrd (package) 16, 18, 20, 22, safety-related ...... 38 \sup (sup) ...... 27 24, 26, 27, 29, 30, 49, 56, 57 scientific ...... 36–38 superscripts \StoneMan () ...... 47 subset and superset 22, 23 new symbols used in . . . 50 \Stopsign ( ) ...... 38 technological . . . . . 36–38 ! supersets ...... 22, 23 T Xbook ...... 43, 45 \StopWatchEnd () ...... 47 \Supset () ...... 23 E variable-sized . . . . . 17–19 \Supset ( ) ...... 22 \StopWatchStart ( ) . . . . . 47 c weather ...... 46 h \supset () ...... 23 \stress ( ) ...... 12 zodiacal ...... 37 \supset (⊃) ...... 22 \strictfi (K) ...... 21 symbols.tex (file) . . . . . 48, 56 \supseteq ( ) ...... 23 \strictif (J) ...... 21 \SYN () ...... 38 \strictiff (L) ...... 21 \supseteq (⊇) ...... 22 () ...... 23 \StrokeFive (;) ...... 47 \supseteqq T \supseteqq ( ) ...... 22 :::: k \T ...... 8 \StrokeFour ( ) ...... 47 \supsetneq ( ) ...... 23 \t (a) ...... 10 \StrokeOne (:) ...... 47 \supsetneq ()) ...... 22 tacks ...... 20, 29 ::: \StrokeThree ( ) ...... 47 \supsetneqq ( ) ...... 23 \taild () ...... 10 \StrokeTwo (::) ...... 47 \supsetneqq (%) ...... 22 \tailinvr (H) ...... 10 \STX () ...... 38 \supsetplus ( ) ...... 22 \taill (0) ...... 10 E \SUB (→) ...... 38 \supsetpluseq ( ) ...... 22 \tailn (9) ...... 10 √ G subscripts \surd ( ) ...... 33 \tailr (F) ...... 10 new symbols used in . . . 50 \SurveySign () ...... 47 \tails (L) ...... 10 \Subset () ...... 23 \Swarrow (w) ...... 26 \tailt (P) ...... 10 Ö \Subset (b) ...... 22 \swarrow ( ) ...... 26 \tailz (_) ...... 10 \subset () ...... 23 \swarrow (.) ...... 25 \talloblong ( ) ...... 16 \subset (⊂) ...... 22 swung dash ...... see \sim tally markers .8 ...... 47 \subseteq () ...... 23 \syllabic (j) ...... 12 \tan (tan) ...... 27 \subseteq (⊆) ...... 22 Symbol ...... 48 \tanh (tanh) ...... 27 \subseteqq () ...... 23 symbols \Tape ( ) ...... 44 \subseteqq ( ) ...... 22 alpine ...... 47 j \subsetneq () ...... 23 APL ...... 37 \Taschenuhr ( ) ...... 47 \subsetneq ( ) ...... 22 astrological ...... 37 \tau (τ) ...... 28 ( Q \subsetneqq () ...... 23 astronomical . . . . . 36, 37 \Taurus ( ) ...... 37 \Taurus ( ) ...... 37 \subsetneqq ($) ...... 22 biological ...... 38 á \subsetplus ( ) ...... 22 body-text ...... 7–14 \taurus ( ) ...... 37 \subsetpluseqD( ) ...... 22 clock ...... 47 \tauup (τ)] ...... 28 subsets ...... F ...... 22, 23 communication ...... 38 \tccentigrade ( ) ...... 34 µ \succ ( ) ...... 20 computer hardware . . . . 37 \tcmu ( ) ...... 34 W \succapprox (Ç) ...... 21 contradiction . . . . . 15, 27 \tcohm ( ) ...... 34 \succapprox ( ) ...... 20 currency ...... 12, 13 \tcpertenthousand ( ) . . 34 v \succcurlyeq (¥) ...... 21 dangerous bend ...... 43 \tcperthousand ( ) ...... 34 technological symbols . . 36–38 \succcurlyeq (<) ...... 20 definition ...... 15 \succdot (Í) ...... 21 dictionary . . see symbols, \Telefon (T) ...... 38 \succeq () ...... 20 phonetic \Telephone (() ...... 47 \succeqq () ...... 21 dingbat ...... 39–44 \Tent () ...... 47 \succnapprox (Ë) ...... 22 dot ...... 33 \tesh (Q) ...... 10 \succnapprox () ...... 20 electrical ...... 36 TEX ...... 48, 50, 52, 53, 57 \succneq () ...... 22 engineering ...... 36, 38 TEXbook, The ...... 50–52

71 symbols from . . . . . 43, 45 \textcopyleft («) ...... 13 \textfrak ...... 35 \text ...... 15, 51 \textcopyright (©) . 7, 13, 55 \textg (¥) ...... 9 \textacutedbl () ...... 12 \textcorner (^)...... 9 \textgamma (G) ...... 9 \textacutemacron (a©¡) . . . . . 11 \textcrb ( ) ...... 9 \textglobfall () ...... 9 \textacutewedge (a§¡) ...... 11 \textcrd (¡) ...... 9 \textglobrise () ...... 9 \textadvancing (a) ...... 11 \textcrg (g) ...... 9 \textglotstop (P) ...... 8 \textasciiacute (´) . . . 12, 55 \textcrh (è) ...... 9 \textgravecircum (a) . . . . . 11 \textasciibreve () ...... 12 \textcrinvglotstop (Û) . . . . 9 \textgravedbl () ...... 12 \textasciicaron () ...... 12 \textcrlambda (¬) ...... 9 \textgravedot (a) ...... 11 \textasciicircum (ˆ) . . . 7, 53 \textcrtwo (2) ...... 9 \textgravemacron (a© ) . . . . . 11 \textasciidieresis (¨) 12, 55 \textctc (C) ...... 9 \textgravemid (a) ...... 11 \textasciigrave (`) ...... 12 \textctd (¢)...... 9 \textgreater (>) . . . 7, 53, 54 \textasciimacron ...... 54 \textctdctzlig (¢ý) ...... 9 \textguarani () ...... 12 \textasciimacron (¯) . 12, 55 \textctesh (²) ...... 9 \texthalflength (;) ...... 8 \textasciitilde (˜) . . . . 7, 53 \textctj (J) ...... 9 \texthardsign (») ...... 8 \textasteriskcentered (*) . 7, \textctn (®)...... 9 \texthooktop (#) ...... 8 14 \textctt (´) ...... 9 \texthtb (á) ...... 8 \textbabygamma (È) ...... 8 \textcttctclig (´C) ...... 9 \texthtbardotlessj (ê) . . . . . 8 \textbackslash (\) . . 7, 53, 54 \textctyogh (¸) ...... 9 \texthtc (Á) ...... 8 \textbaht () ...... 12 \textctz (ý) ...... 9 \texthtd (â) ...... 8 ¤ ä \textbar (|) ...... 7, 53, 54 \textcurrency ( ) . . . . 12, 55 \texthtg ( ) ...... 9 H \textbarb (b) ...... 8 \textdagger ( ) ...... 7, 14 \texthth ( ) ...... 9 Ê \textbarc (c) ...... 8 \textdaggerdbl ( ) . . . . . 7, 14 \texththeng ( ) ...... 9 Î \textbard (d)...... 8 \texthtk ( ) ...... 9 ( ) ...... 43 Ò \textbardbl () ...... 14 \textdbend \texthtp ( ) ...... 9 (-) ...... 14 Ó \textbardotlessj (é) ...... 8 \textdblhyphen \texthtq ( ) ...... 9 \textdblhyphenchar () . . . . 14 £ \textbarg (g) ...... 8 \texthtrtaild ( ) ...... 9 \textdctzlig (dý) ...... 9 É \textbarglotstop (Ü) ...... 8 \texthtscg ( ) ...... 9 \textdegree (°) ...... 34, 55 Ö \textbari (1) ...... 8 \texthtt ( ) ...... 9 \textdied (d) ...... 45 ÿ \textbarl (ª) ...... 9 \texthvlig ( ) ...... 9 \textdiscount () ...... 14 \textbaro (8) ...... 9 \textifsym ...... 36 \textdiv (ö) ...... 34 \textbarrevglotstop (Ý) . . . 9 \textinterrobang ( ) . . . . . 14 \textdivorced (c) ...... 45 () . . 14 \textbaru (0) ...... 9 \textinterrobangdown \textdollar ($) ...... 7, 12 (Û) ...... 9 \textbeltl (ì) ...... 9 \textinvglotstop \textdollaroldstyle () . . 12 \textinvscr (K) ...... 9 \textbeta (B) ...... 9 \textdong () ...... 12 \textinvsubbridge (a) . . . . 11 \textbigcircle (O) ...... 14 \textdotacute (a) ...... 11 \textiota (Ì) ...... 9 \textblank ( ) ...... 14 \textdotbreve (a¨ ) ...... 11 \textlambda («) ...... 9 \textborn (b) ...... 45 \textdoublebaresh (S) . . . . . 9 \textlangle (<) ...... 31, 53 \textbottomtiebar (a) . . . . 11 < \textdoublebarpipe (}) . . . . 9 \textlbrackdbl ([) ...... 31 \textbraceleft ({) ...... 7 \textdoublebarslash (=/ ) . . . 9 \textleaf (l) ...... 45 \textbraceright (}) ...... 7 \textdoublegrave (a ) . . . . . 11 \textleftarrow () ...... 25 ©¨ \textbrevemacron (a) . . . . . 11 \textdoublepipe ({) ...... 9 \textlengthmark (:) ...... 9 ¦ \textbrokenbar ( ) . . . . 14, 55 \textdoublevbaraccent (a) . 11 \textless (<) . . . . . 7, 53, 54 \textbullet ( ) ...... 7, 14 \textdoublevertline () . . . 9 ~ \textbullseye (ò) ...... 9 \textdownarrow (_) ...... 25 \textlhdbend ( ) ...... 43 \textcelsius () ...... 36 \textdownstep ()...... 9 \textlhookt (³) ...... 9 \textceltpal ( ) ...... 9 \textdyoghlig (Ã) ...... 9 \textlhtlongi (¦) ...... 9 \textcent (¢) ...... 12, 55 \textdzlig (dz)...... 9 \textlhtlongy (¶) ...... 9 \textcentoldstyle () . . . . 12 \texteightoldstyle (8) . . . 13 \textlira () ...... 12 \textchi (X) ...... 9 \textellipsis (. . . ) ...... 7 \textlnot (¬) ...... 34, 55 \textcircled (O) ...... 10 \textemdash (—) ...... 7 \textlonglegr (Ô) ...... 9 \textcircledP () ...... 13 \textendash (–) ...... 7 \textlowering (a) ...... 11 \textcircumacute (a) . . . . . 11 \textepsilon (E) ...... 9 \textlptr (½) ...... 9 \textcircumdot (a¢ ) ...... 11 \textesh (S) ...... 9 \textlquill ( ) ...... 31 \textcloseepsilon (Å) . . . . . 9 \textestimated () ...... 14 \textltailm (M) ...... 9 \textcloseomega (Ñ) ...... 9 \texteuro (¿) ...... 12 \textltailn (ñ) ...... 9 \textcloserevepsilon (Æ) . . . 9 \textexclamdown (¡) ...... 7 \textltilde (ë) ...... 9 \textcolonmonetary () . . . 12 \textfishhookr (R) ...... 9 \textlyoghlig (Ð) ...... 9 \textcommatailz (Þ) ...... 9 \textfiveoldstyle (5) . . . . 13 \textmarried (m) ...... 45 textcomp (package) ...... 6, \textflorin ()...... 12 \textmho (M) ...... 36 7, 10, 12–14, 25, 31, 34, 36, \textfouroldstyle (4) . . . . 13 \textmidacute (a) ...... 11 45, 48, 54, 56, 57 \textfractionsolidus (/) . . 34 \textminus (=) ...... 34

72 \textmu (µ) ...... 36, 55 \textrhookschwa (Ä) ...... 9 \texttctclig (tC) ...... 9 \textmusicalnote (n) . . . . . 14 \textrhoticity (~) ...... 9 \textteshlig (Ù) ...... 9 \textnaira () ...... 12 \textrightarrow () . . . . . 25 \texttheta (T) ...... 9 \textnineoldstyle (9) . . . . 13 \textringmacron (¦a©) ...... 11 \textthorn (þ) ...... 9 \textnumero () ...... 14 \textroundcap (a) ...... 11 \textthreeoldstyle (3) . . . 13 \textObardotlessj (Í) . . . . . 9 \textrptr (¾) ...... 9 \textthreequarters (¾) 34, 55 \textohm (W) ...... 36 \textrquill (¡) ...... 31 \textthreequartersemdash () \textOlyoghlig () ...... 9 \textrtaild (ã) ...... 9 ...... 14 \textomega (°) ...... 9 \textrtaill (í)...... 9 \textthreesuperior (³) 34, 55 \textonehalf (½) . . . . . 34, 55 \textrtailn (ï) ...... 8 \texttildedot (a£ ) ...... 12 \textoneoldstyle ...... 13 \textrtailr (ó) ...... 8 \texttildelow (~) ...... 12 \textoneoldstyle (1) . . . . . 13 \textrtails (ù) ...... 8 \texttimes (Ö) ...... 34 \textonequarter (¼) . . . 34, 55 \textrtailt (ú) ...... 8 \texttoneletterstem (¿) . . . . 9 > \textonesuperior (¹) . . 34, 55 \textrtailz (ü) ...... 8 \texttoptiebar (a) ...... 12 \textopenbullet () ...... 14 \textrthook ($) ...... 8 \texttrademark () . . . . 7, 13 \textopencorner (_) ...... 9 \textsca (À) ...... 8 \texttslig (µ) ...... 9 \textopeno (O) ...... 9 \textscb (à) ...... 8 \textturna (5) ...... 9 \textordfeminine (ª) 7, 14, 55 \textsce (¤) ...... 9 \textturncelig (¯) ...... 9 \textordmasculine (º) 7, 14, 55 \textscg (å) ...... 9 \textturnh (4) ...... 9 \textovercross (a) ...... 11 \textsch (Ë) ...... 9 \textturnk (©) ...... 9 \textoverw (a) ...... 11 \textschwa (@) ...... 9 \textturnlonglegr (Õ) . . . . . 9 % \textpalhook ( ) ...... 9 \textsci (I) ...... 9 \textturnm (W) ...... 9 ¶ \textparagraph ( ) . . . . 7, 14 \textscj (¨) ...... 9 \textturnmrleg (î) ...... 9 · \textperiodcentered ( ) . 7, 14, \textscl (Ï) ...... 9 \textturnr (ô) ...... 9 55 \textscn (ð) ...... 9 \textturnrrtail (õ) ...... 9 \textpertenthousand ( ) . 14 \textscoelig (×) ...... 9 \textturnscripta (6) ...... 9 \textperthousand ( ) . . . . 14 \textscomega (±) ...... 9 \textturnt (Ø) ...... 9 \textpeso ( ) ...... 12 \textscr (ö) ...... 9 \textturnv (2) ...... 9 F \textphi ( )...... 9 \textscripta (A) ...... 9 \textturnw (û) ...... 9 \textpilcrow ( ) ...... 14 \textscriptg (g) ...... 9 \textturny (L) ...... 9 | \textpipe ( ) ...... 9 \textscriptv (V) ...... 9 \texttwelveudash () . . . . . 14 ± \textpm ( ) ...... 34, 55 \textscu (Ú) ...... 9 \texttwooldstyle ...... 13 (a ) ...... 11 \textpolhook \textscy (Y) ...... 9 \texttwooldstyle (2) . . . . . 13 \textprimstress (") ...... 9 \textseagull (a) ...... 11 \texttwosuperior (²) . . 34, 55 \textquestiondown (¿) . . . . . 7 \textsecstress () ...... 9 \textunderscore ( ) ...... 7 \textquotedbl (") . . . . . 8, 53 \textsection (§) ...... 7, 14 \textuparrow (^) ...... 25 \textquotedblleft (“) . . . . . 7 \textservicemark () . . . . . 13 \textupsilon (U) ...... 9 \textquotedblright (”) . . . . 7 \textsevenoldstyle (7) . . . 13 \textupstep () ...... 9 \textquoteleft (‘) ...... 7 \textsixoldstyle (6) . . . . . 13 \textvbaraccent (a) ...... 12 \textquoteright (’) ...... 7 \textsoftsign (º)...... 9 \textvertline () ...... 9 \textquotesingle (') . . . . . 14 \textsterling (£) . . . . . 7, 12 \textvibyi (§) ...... 9 \textquotestraightbase ( ) 14 \textstretchc (Â) ...... 9 \textvibyy (·) ...... 9 \textquotestraightdblbase () \textsubacute (a) ...... 11 \textvisiblespace ( ) . . . . . 7 ...... 14 \textsubarch (a) ...... 11 \textwon () ...... 12 \textraiseglotstop (¼) . . . . 9 \textsubbar (a) ...... 11 \textwynn (ß) ...... 9 \textraisevibyi (§) ...... 9 © \textsubbridge (a) ...... 11 \textyen (¥) ...... 12, 55 \textraising (a) ...... 11 \textsubcircum (a) ...... 11 \textyogh (Z) ...... 9 \textramshorns (7) ...... 9 ¢ \textsubdot (a) ...... 11 \textzerooldstyle (0) . . . . 13 \textrangle (>) ...... 31, 53 \textsubgrave (a) ...... 11 \TH (Þ) ...... 7 \textrbrackdbl (]) ...... 31 (a) . . . . 11 \th (þ) ...... 7 \textrecipe () ...... 14, 50 \textsublhalfring Thành,HànThê´ ...... 52 \textreferencemark (¸) 14, 15 \textsubplus (a) ...... 11 (6) ...... 21 \textregistered (®) 7, 13, 55 \textsubrhalfring (a) . . . . 11 \therefore ( ) ...... 20 \textretracting (a) ...... 11 \textsubring (a) ...... 11 \therefore ∴ ¦ \textrevapostrophe (\) . . . . . 9 \textsubsquare (a) ...... 11 \Thermo ...... 46 \textsubtilde (a) ...... 11 \Theta (Θ) ...... 28 \textreve (9) ...... 9 £ \textsubumlaut (a) ...... 11 \theta (θ) ...... 28 \textrevepsilon (3) ...... 9 ¤ θ \textsubw (a) ...... 11 \thetaup ( ) ...... 28 \textsubwedge (a) ...... 12 \thickapprox ( ) ...... 20 \textreversedvideodbend ( ) § ≈ ...... 43 \textsuperimposetilde (a&) . 12 \thicksim (∼) ...... 20 \textrevglotstop (Q) ...... 9 \textsurd (») ...... 34 \thickvert (~) ...... 30 \textrevyogh (¹) ...... 9 \textswab ...... 35 \ThinFog () ...... 46 \textrhookrevepsilon (Ç) . . 9 \textsyllabic (a) ...... 12 \third (3) ...... 34 "

73 \Thorn ( ) ...... 8 \underbrace (|{z}) ...... 31 \varcurlyvee ( ) ...... 16 \thorn (B) ...... 10 \varcurlywedge( ) ...... 16 Þ \underbracket ...... 51, 52 \thorn ( ) ...... 8 \vardiamondsuit ( ) ...... 34 \underbracket ( ) ...... 52 q \tilde (þ˜) ...... 31, 52 \varEarth (J) ...... 37 \tildel (-) ...... 10 \underdots (r) ...... 12 \varepsilon (ε) ...... 28 time of day ...... 47 \undergroup (loooon) ...... 32 \varepsilonup (ε) ...... 28 Times ...... 13 \underleftarrow ( ) . . . . . 32 \VarFlag () ...... 47 \times (×) ...... 15 ←− \underleftrightarrow ( ) 32 varg (txfonts/pxfonts package op- tipa (package) 8, 9, 11, 12, 56, 57 ←→ tion) ...... 28 \underline ( ) ...... 31 \to ...... see \rightarrow \varg (1) ...... 28 \underparenthesis . . . . 51, 52 \ToBottom (½) ...... 46 \vargeq (©) ...... 24 \underparenthesis ( ) . . . 52 \tone ...... 9 |} \varhash (#) ...... 34 \top (>) ...... 29, 50 ( ) . . . . 32 \underrightarrow −→ \varheartsuit (r) ...... 34 \topbot (⊥>) ...... 50 \underring (y) ...... 12 \varhexagon ( ) ...... 42 \topdoteq () ...... 21 underscore ...... see \_ \varhexstar (9) ...... 41 \ToTop ( ) ...... 46 ¼ \undertilde (|) ...... 12 variable-sized symbolsB . . 17–19 trademark . see \texttrademark \underwedge (}) ...... 12 \VarIceMountain () . . . . . 47 \triangle (4) ...... 33 union ...... see \cup \varinjlim (lim) ...... 28 triangle relations ...... 24 −→ unity (1).. see alphabets, math \varint ( ) ...... 18 \TriangleDown (3) ...... 42 r \unlhd (E) ...... 15, 16 \varkappa (κ) ...... 28 o 3 \TriangleDown ( vs. ) . . 49 \unrhd (D) ...... 15, 16 \varleq (¨) ...... 24 \TriangleDown (o) ...... 43 \UParrow ( ) ...... 45 \varliminf (lim) ...... 28 \triangledown (O) ...... 33 \Uparrow (K⇑) ...... 25, 30 \varlimsup (lim) ...... 28 \TriangleLeft (2) ...... 42 \uparrow (↑) ...... 25, 30 \varmathbb ...... 35 \triangleleft () ...... 24 \upbracketfill ...... 52 \VarMountain () ...... 47 \triangleleft (/) ...... 15 \Updownarrow (m) . . . . . 25, 30 \varnothing (∅) ...... 33 \trianglelefteq () . . . . . 24 \updownarrow (l) . . . . . 25, 30 \varnotin (T) ...... 29 Ö \trianglelefteq ( ) . . . . . 24 \updownarrows ( ) ...... 26 \varnotowner (U) ...... 29 E ê \trianglelefteqslant ( ) . 24 \updownharpoons ( ) ...... 27 \varoast ( ) ...... 16 P \upharpoonleft (ä) ...... 27 \varobar () ...... 16 \triangleq (,) ...... 15, 24 \upharpoonleft () ...... 25 \varobslash ( ) ...... 16 \TriangleRight (4) ...... 42 \upharpoonright (æ) ...... 27 \varocircle () ...... 16 \triangleright () ...... 24 \upharpoonright () ...... 25 \varodot ( ) ...... 16 \triangleright (.) ...... 15 \uplus (Z) ...... 17 \varogreaterthan ( ) . . . . 16 \trianglerighteq () . . . . 24 \uplus (]) ...... 15 5 ( ) . 19 \trianglerighteq ( ) . . . . 24 \varoiiintclockwise D \upp (t) ...... 12 \trianglerighteqslant ( ) 24 \varoiiintctrclockwise ( ) \upparenthfill ...... 52 triangles ...... 33,Q 42, 43 . . . . .! . . . . 19 F upquote (package) ...... 53 \varoiint ( ) ...... N . . 19 \TriangleUp (1) ...... 42 upright Greek letters ...... 28 \varoiintclockwise ( ) . . 19 \TriangleUp (n vs. 1) . . . . 49 \Upsilon (Υ) ...... 28 \varoiintctrclockwise ( ) 19 \TriangleUp (n) ...... 43 \upsilon (υ) ...... 28 υ \varoint ( ) . . . . .B ...... 18 \Tsteel (œ) ...... 38 \upsilonup ( ) ...... 28 u l \varointclockwise ( ) .J . . . 19 \TTsteel (š) ...... 38 \upt ( ) ...... 12 þ \varointclockwise ( ) . . . . 19 \Tumbler () ...... 46 \uptodownarrow ( ) ...... 26 Ò \TwelweStar (J) ...... 41 \upuparrows ( ) ...... 26 \varointctrclockwise- ( ) . 19 \twoheadleftarrow ( ) . . . 25 \upuparrows () ...... 25 \varointctrclockwise ( ) . . 19 Ú \twoheadrightarrow ( ) . . 25 \upupharpoons ( ) ...... 27 \varolessthan ( ) . . .+ . . . . 16 G 4 \twonotes ( ) ...... 45 \Uranus ( ) ...... 37 \varominus ( ) ...... 16 \Uranus ( )...... 36 txfonts (package) . 15, 16, 19–29, Ç \varoplus ( ) ...... 16 33–35, 48, 50, 56, 57 \uranus ( ) ...... 36 \varoslash ( ) ...... 16 \urcornerZ(y) ...... 29 \varotimes () ...... 16 U \urcorner (q) ...... 29 \varovee ( ) ...... 16 \U (¼a) ...... 10 url (package) ...... 53 \varowedge6( ) ...... 16 \u (˘a) ...... 10 \US ( ) ...... 38 \varparallel7(∥) ...... 21 \udot (¤) ...... 17 \usepackage ...... 6 \varparallelinv ( ) ...... 21 \ulcorner (x) ...... 29 \varphi (ϕ) ...... 28 \ulcorner (p) ...... 29 V \varphiup (ϕ) ...... 28 ulsy (package) ...... 17, 27, 56 \v (ˇa) ...... 10 \varpi ($) ...... 28 umlaut ...... see accents \varangle ( ) ...... 34 \varpiup ($) ...... 28 \underaccent ...... 52 \varbigcirc( ) ...... 16 \varprod ( ) ...... 19 , \varprojlim (lim) ...... 28 \underarch (a) ...... 12 \VarClock ( ) ...... 47 ←− loomoon \underbrace ( ) ...... 32 \varclubsuit (p) ...... 34 \varpropto(∝) ...... 20

74 \varrho (%) ...... 28 \veebar (Y) ...... 15 \widetilde (e) ...... 31 \varrhoup (%) ...... 28 \veedoublebar ([) ...... 17 \widetriangle (æ) ...... 31 \varsigma (ς) ...... 28 \Venus (B ) ...... 37 \wind ...... 46 \varsigmaup (ς) ...... 28 \Venus (Ã) ...... 36 Windows ...... 54 \varspadesuit (s) ...... 34 \venus ( ) ...... 36 \Womanface (þ) ...... 46 \varsqsubsetneq () . . . . . 23 \vernal ♀( ) ...... 36 \wp (℘) ...... 29 \varsqsubsetneqq () . . . . 23 \Vert (k) ...... 30 \wr (o) ...... 15 \varsqsupsetneq () . . . . . 23 \vert (|) ...... 30 wreath product ...... see \wr \varsqsupsetneqq ( ) . . . . 23 \VHF ( ) ...... 36 \Writinghand (b) ...... 43 \varstar () ...... 17 \Village@ ( ) ...... 47 wsuipa (package) 10, 12, 49, 52, \varsubsetneq () ...... 23 \Virgo ( ) ...... 37 56 \varsubsetneq ( ) ...... 22 å \virgo ( ) ...... 37 \varsubsetneqq () ...... 23 \VT (♂) ...... 38 X \varsubsetneqq ( ) ...... 22 #» ` & \vv ( ) ...... 32 \XBox ( ) ...... 41 \VarSummit ( ) ...... 47 \VvDash () ...... 21 \Xi (Ξ)4 ...... 28 \varsupsetneq ( ) ...... 23 \Vvdash (,) ...... 21 \xi (ξ) ...... 28 \varsupsetneq ( ) ...... 22 \xiup (ξ) ...... 28 ! \Vvdash () ...... 20 () ...... 23 \varsupsetneqq \vvvert (~) ...... 30 \xleftarrow (←−) ...... 32 ( ) ...... 22 \varsupsetneqq ' XML ...... 54 W () ...... 47 \VarTaschenuhr \WashCotton ( ) ...... 46 \xrightarrow (−→) ...... 32 (ϑ) ...... 28 ‰ \vartheta \WashSynthetics ( ) . . . . 46 Xs ...... 40, 41, 43 (ϑ) ...... 28 Š \varthetaup \WashWool ( ) ...... 46 \XSolid (#) ...... 40 \vartimes ( ) ...... 16 ‹ \wasylozenge ( ) ...... 45 \XSolidBold ($) ...... 40 " ( ) ...... 33 \vartriangle M \wasypropto ( ) ...... 20 ◊ \XSolidBrush (%) ...... 40 \vartriangleleft ( ) . . . . 24 wasysym (package) 8, 13–16, 18, XY-pic ...... 51 \vartriangleleft (C) . . . . 24 20, 22, 23, 25, 33, 34, 36–38, \vartriangleright ( ) . . . . 24 41, 42, 45, 49, 56, 57 ( ) . . . . 24 Y \vartriangleright B \wasytherefore ( ) ...... 34 \varv (3) ...... 28 \Ydown ( ) ...... 16 () .∴ ...... 46 \varw (4) ...... 28 \WeakRain yfonts (package) . . . . . 35, 56, 57 () ...... 46 \vary (2) ...... 28 \WeakRainCloud yhmath (package) . 31, 33, 51, 56 weather symbols ...... 46 \VBar ()...... 42 \Yinyang (Y) ...... 46 \VDash (() ...... 21 \Wecker ( ) ...... 47 \Yleft ( ) ...... 16 ^ ` \Vdash (,) ...... 21 \wedge ( ) ...... 17 \yogh ( ) ...... 10 \Vdash ( ) ...... 20 \wedge (∧) ...... 15 \Yright ( ) ...... 16 \vDash (() ...... 21 Weierstrass ℘ function . see \wp \Yup ( ) ...... 16 \vDash ( ) ...... 20 \Wheelchair (w) ...... 43 t \vdash (`) ...... 20 \widearrow ( ) ...... 32 Z s . \widebar ( ) ...... 32 Zapf Chancery ...... 35 \vdots (.) ...... 33 \widecheck (q) ...... 32 Zapf Dingbats ...... 39, 41 \vec (~) ...... 31 \widehat (b) ...... 31 zapfchan (package) ...... 56 u \Vectorarrow (p) ...... 34 \wideparen ( ) ...... 32 \Zborder (Z) ...... 43 ó \Vectorarrowhigh (P) ...... 34 \wideparen ( ) ...... 31 \zeta (ζ) ...... 28 \vee (_) ...... 17 \widering (˚ó) ...... 32 \zetaup (ζ) ...... 28 \vee (∨) ...... 15 ˚ \Zodiac ...... 37 \veebar (Y) ...... 17 \widering (ó) ...... 31 zodiacal symbols ...... 37