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Braille Mathematics Notation BRAILLE AUTHORITY OF THE UNITED KINGDOM BRAILLE MATHEMATICS NOTATION Royal National Institute of the Blind Bakewell Road Orton Southgate Peterb orough Cambridgeshire PE XU c Braille Authority of the United Kingdom Registered Charity No Printed by RNIB Peterb orough CONTENTS Memb ers of the Mathematics Committee ii Memb ers of the JointTechnical Committee ii Intro duction to edition iii Intro duction to edition iv Table of braille mathematical signs Mo dication of signs Braille Mathematics Notation General remarks Numeral and letter signs The spacing of braille signs The oblique stroke and fraction line Brackets Indices Sp ecial functions and other words and abbreviations Delimiting the argument of a function Co ordinates and sets Matrices determinants and other arrays Worked calculations logical gures Miscellaneous notation Layout of mathematical text Units Alphab ets used in mathematics Index i MEMBERS OF THE MATHEMATICS COMMITTEE A W Chatters Chairman Bristol University J A Allnut Central Electricity Research Lab oratory T K Devonald Royal National College for the Blind J Fullwo o d Marconi Systems T D Maley Braille House RNIB Miss D M Nicholl Braille House RNIB S J Phipp en Braille House RNIB W B L Po ole Chairman Braille Authority of the United Kingdom Miss J Short Chorleywo o d College D Spyb eyWorcester College PJTalb ot Principal Queen Alexandra College MEMBERS OF THE JOINT TECHNICAL COMMITTEE D Bo den Braille Computer Asso ciation of the Blind N Brown New College Worcester S A Clamp Visual Impairment and Sp ecial Needs Advice VISpA S J Phipp en RNIB Peterb orough W B L Po ole Chairman Braille Authority of the United Kingdom D Spyb ey New College Worcester P Southall Dorton House Scho ol C Stonehouse New College Worcester PTo oze Pia M E Townsend TorchTrust for the Blind R West Braille Computer Asso ciation of the Blind ii INTRODUCTION TO EDITION This edition of the Brail le Mathematics Notation has b een prepared by the Mathemat ics Committee of the Braille Authority of the United Kingdom It arose from the need to extend and amend the edition in print the edition with Addendum and this also seemed to b e a go o d o ccasion to rewrite the co de b o ok in a more convenient form It should b e emphasized that no changes have b een made in such basic notations as those for addition subtraction multiplication division brackets equality unions intersections inequalities and so on Two of the most imp ortantchanges made in this edition are concerned with unit ab breviations and with letter fount conventions The abbreviations for such units as metre second and gram will now follow the numb er of units rather than precede it so that braille will follow the standard print convention The rules ab out fount indicators have b een changed so that letters will now b e assumed to b e small Latin unless shown otherwise Another imp ortantchange is the extension of the use of the sign to co de any sort of sp ecial function eg lim exp det etc as well as the trigonometric and hyp erb olic functions At the same time some of the old word abbreviations suchas for rectangle have b een deleted A few alterations have b een made in order to simplify the rules and increase conceptual clarityFor example the numerator of a fraction will always b e shown even when it is so that Similarly the exp onent rather than will now b e written will always b e shown so that x will b e written rather than It will no longer b e necessary to decide whether an upp er symbolinprint should b e treated as a sup erscript or as an exp onent the same sup erscript sign will nowserve in b oth cases The sp ecial metho d for dealing with limits of integrals has b een deleted Some new symb ols have b een added to the co de to deal with certain printsymb ols whichwere not catered for b efore There was a strong feeling in the committee that the time had come to rewrite and restructure the co de b o ok The two part structure of the old co de has b een abandoned and it is hop ed that the way the new edition is organized will makeitmuch easier to use Iwould like to thank all the memb ers of the committee for b eing so generous with their time and exp ertise and for making our discussions lively but go o d humoured I am sure that all the other memb ers will join me in expressing our appreciation of the work done by the Braille House sta in pro ducing all the do cuments so eciently in b oth braille and print A W Chatters Bristol November iii INTRODUCTION TO EDITION The current edition of Brail le Mathematics Notation contains some minor amendments to the edition prompted by the publication of the edition of British Brail leThe main issues relate to the new rules on capital indicators For conformity with British Brail le the double capital indicator is now used for a sequence of two or more capital letters rather than for sequences of three or more This change has b een carried through to other fount indicators in this co de as well as to unit abbreviations Also single capital letters standing alone or starting a mathematical expression in ordinary text now require a letter sign b efore the capital sign as in British Brail lethus removing a p ossible ambiguity with single letter wordsigns in line with British The oblique stroke has b een changed to the cell sign Brail le The force of the numeral sign no longer carries over the hyphen again in line with British Brail le Unit abbreviations starting with a lower case letter followed by a capital letter such as mW now require a letter sign b efore the m whichwas previously not the case June iv TABLE OF BRAILLE MATHEMATICAL SIGNS The braille signs in the following table should generally b e used to representthe corresp onding print signs whatever their meaning In a few cases however more than one braille sign has the same print equivalent eg the signs for for these the correct braille sign should b e used according to the meaning or use stated in brackets Sign Meaning Sign Meaning plus minus or approximately equal to multiplied by cross divided by varies as prop ortional to plus or minus is dened as Def minus or plus is pro jective with oblique stroke fraction line sign less than continued fraction symbol less than or equal to multiplication dot and greater than in logic greater than or equal to etc an op eration sign eg x y much less than etc a second much greater than op eration sign greater than or less than p ro ot less than or equals approximately equal to greater than or equivalent to approximately equal to swung dash numeral sign Table of Brail le Mathematical Signs Sign Meaning Sign Meaning decimal p oint intersection comma or space marking union thousands etc and meet vector pro duct recurring decimal sign or join bar over negative numb er eg n set dierence contained in contains containedinor equal to contains or equal to f is an elementof g reverse of angle bracket not angle bracket amp ersand and j vertical bar mo dulus determinant for all such that divides restricted to there exists evaluated at etc empty set k double vertical bar norm is a theorem matrix bracket a reverse of therefore jisvalid since reverse of j Table of Brail le Mathematical Signs Sign Meaning Sign Meaning sup erscript or subscript arrow indicating vector eg AB sin sup erscript or subscript arrow indicating vector sin arcsin eg AB cos arrow with long shaft cos arccos arrow with long shaft tan tan arctan sec sec arcsec cosec cosec arccosec cot cot arccot sinh sinh arcsinh cosh cosh arccosh tanh Table of Brail le Mathematical Signs Sign Meaning Sign Meaning is a normal subgroup of tanh arctanh or equal to sech reverse of sech arcsech k parallel symbol cosech p erp endicular symb ol cosech arccosech R integral coth H closed line integral coth arccoth innity log t etc end of pro of log antilog hash colog factorial grad gradient point notation of curl or rot partial correlation or regression in div divergence statistics eg
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