Numbers 1 to 100 PDF generated using the open source mwlib toolkit. See http://code.pediapress.com/ for more information. PDF generated at: Tue, 30 Nov 2010 02:36:24 UTC Contents Articles −1 (number) 1 0 (number) 3 1 (number) 12 2 (number) 17 3 (number) 23 4 (number) 32 5 (number) 42 6 (number) 50 7 (number) 58 8 (number) 73 9 (number) 77 10 (number) 82 11 (number) 88 12 (number) 94 13 (number) 102 14 (number) 107 15 (number) 111 16 (number) 114 17 (number) 118 18 (number) 124 19 (number) 127 20 (number) 132 21 (number) 136 22 (number) 140 23 (number) 144 24 (number) 148 25 (number) 152 26 (number) 155 27 (number) 158 28 (number) 162 29 (number) 165 30 (number) 168 31 (number) 172 32 (number) 175 33 (number) 179 34 (number) 182 35 (number) 185 36 (number) 188 37 (number) 191 38 (number) 193 39 (number) 196 40 (number) 199 41 (number) 204 42 (number) 207 43 (number) 214 44 (number) 217 45 (number) 220 46 (number) 222 47 (number) 225 48 (number) 229 49 (number) 232 50 (number) 235 51 (number) 238 52 (number) 241 53 (number) 243 54 (number) 246 55 (number) 248 56 (number) 251 57 (number) 255 58 (number) 258 59 (number) 260 60 (number) 263 61 (number) 267 62 (number) 270 63 (number) 272 64 (number) 274 66 (number) 277 67 (number) 280 68 (number) 282 69 (number) 284 70 (number) 286 71 (number) 289 72 (number) 292 73 (number) 296 74 (number) 298 75 (number) 301 77 (number) 302 78 (number) 305 79 (number) 307 80 (number) 309 81 (number) 311 82 (number) 313 83 (number) 315 84 (number) 318 85 (number) 320 86 (number) 323 87 (number) 326 88 (number) 328 89 (number) 333 90 (number) 335 91 (number) 337 92 (number) 340 93 (number) 343 94 (number) 346 95 (number) 349 97 (number) 352 98 (number) 354 99 (number) 356 100 (number) 358 101 (number) 361 1000 (number) 363 List of numbers 373 Number names 391 References Article Sources and Contributors 399 Image Sources, Licenses and Contributors 412 Article Licenses License 415 −1 (number) 1 −1 (number) −1 −1 0 1 2 3 4 5 6 7 8 9 → List of numbers — Integers 0 10 20 30 40 50 60 70 80 90 → Cardinal −1, minus one, negative one ١− Arabic Chinese numeral 负一，负弌，负壹 Bengali ô১ Binary (byte) S&M: 100000001 2 2sC: 11111111 2 Hex (byte) S&M: 0x101 8 2sC: 0xFF 8 In mathematics, −1 is the additive inverse of 1, that is, the number that when added to 1 gives the additive identity element, 0. It is the negative integer greater than negative two (−2) and less than 0. Negative one has some similar but slightly different properties to positive one.[1] Negative one bears relation to Euler's identity since e iπ = −1. In computer science, −1 is a common initial value for integers and is also used to show that a variable contains no useful information. Algebraic properties Multiplying a number by −1 is equivalent to changing the sign on the number. This can be proved using the distributive law and the axiom that 1 is the multiplicative identity: for x real, we have where we used the fact that any real x times 0 equals 0, implied by cancellation from the equation In other words, so (−1) · x is the arithmetic inverse of x, or −x. −1 (number) 2 Square of −1 The square of −1, i.e. −1 multiplied by −1, equals 1. As a consequence, a product of negative real numbers is positive. For an algebraic proof of this result, start with the equation The first equality follows from the above result. The second follows from the definition of −1 as additive inverse of 1: it is precisely that number that when added to 1 gives 0. Now, using the distributive law, we see that The second equality follows from the fact that 1 is a multiplicative identity. But now adding 1 to both sides of this last equation implies The above arguments hold in any ring, a concept of abstract algebra generalizing integers and real numbers. Square roots of −1 The complex number i satisfies i2 = −1, and as such can be considered as a square root of −1. The only other complex number x satisfying the equation x2 = −1 is −i. In the algebra of quaternions, containing the complex plane, the equation x2 = −1 has an infinity of solutions.[2] Exponentiation to negative integers Exponentiation of a non-zero real number can be extended to negative integers. We make the definition that x−1 = 1/x, meaning that we define raising a number to the power −1 to have the same effect as taking its reciprocal. This definition then extended to negative integers preserves the exponential law xaxb = x(a + b) for a,b non-zero real numbers. Exponentiation to negative integers can be extended to invertible elements of a ring, by defining x−1 as the multiplicative inverse of x. Computer representation There are a variety of ways that −1 (and negative numbers in general) can be represented in computer systems, the most common being as two's complement of their positive form. Since this representation could also represent a positive integer in standard binary representation, a programmer must be careful not to confuse the two. Negative one in two's complement could be mistaken for the positive integer 2n − 1, where n is the number of digits in the representation (that is, the number of bits in the data type). For example, 11111111 (binary) and FF (hex) each 2 16 represents −1 in two's complement, but represents 255 in standard numeric representation. See also • Signed zero References [1] Mathematical analysis and applications (http:/ / books. google. com/ books?id=Xrh89dLWZqEC) By Jayant V. Deshpande, ISBN 1842651897 [2] http:/ / mathforum. org/ library/ drmath/ view/ 58251. html 0 (number) 3 0 (number) 0 −1 0 1 2 3 4 5 6 7 8 9 → List of numbers — Integers 0 10 20 30 40 50 60 70 80 90 → Cardinal 0, zero, "oh" (pronounced /ˈoʊ/), nought, naught, nil. Ordinal 0th, zeroth, noughth Factorization Divisors all numbers Roman numeral N/A 0,٠ Arabic Bengali ০ Devanāgarī ० Chinese 〇，零 Japanese numeral 〇，零 Khmer ០ Thai ๐ Binary 0 Octal 0 Duodecimal 0 Hexadecimal 0 Zero, written 0, is both a number[1] and the numerical digit used to represent that number in numerals. It plays a central role in mathematics as the additive identity of the integers, real numbers, and many other algebraic structures. As a digit, 0 is used as a placeholder in place value systems. In the English language, 0 may be called zero, nought or (US) naught (both pronounced /ˈnɔːt/), nil, or "o". Informal or slang terms for zero include zilch and zip.[2] Ought or aught (both pronounced /ˈɔːt/), have also been used.[3] As a number 0 is the integer immediately preceding 1. In most systems, 0 was identified before the idea of negative things that go lower than zero was accepted. Zero is an even number,[4] because it is divisible by 2. 0 is neither positive nor negative. By some definitions 0 is also a natural number, and then the only natural number not to be positive. Zero is a number which quantifies a count or an amount of null size. The value, or number, zero is not the same as the digit zero, used in numeral systems using positional notation. Successive positions of digits have higher weights, so inside a numeral the digit zero is used to skip a position and give appropriate weights to the preceding and following digits. A zero digit is not always necessary in a positional number system, for example, in the number 02. In some instances, a leading zero may be used to distinguish a number. 0 (number) 4 As a year label In the BC calendar era, the year 1 BC is the first year before AD 1; no room is reserved for a year zero. By contrast, in astronomical year numbering, the year 1 BC is numbered 0, the year 2 BC is numbered −1, and so on.[5] Names In 976 the Persian encyclopedist Muhammad ibn Ahmad al-Khwarizmi, in his "Keys of the Sciences", remarked that if, in a calculation, no number appears in the place of tens, a little circle should be used "to keep the rows". This circle the Arabs called sifr (empty). That was the earliest mention of the name sifr that eventually became zero.[6] Italian zefiro already meant "west wind" from Latin and Greek zephyrus; this may have influenced the spelling when transcribing Arabic ṣifr.[7] The Italian mathematician Fibonacci (c.1170–1250), who grew up in North Africa and is credited with introducing the decimal system to Europe, used the term zephyrum. This became zefiro in Italian, which was contracted to zero in Venetian. As the decimal zero and its new mathematics spread from the Arab world to Europe in the Middle Ages, words derived from ṣifr and zephyrus came to refer to calculation, as well as to privileged knowledge and secret codes. According to Ifrah, "in thirteenth-century Paris, a 'worthless fellow' was called a '... cifre en algorisme', i.e., an 'arithmetical nothing'."[7] From ṣifr also came French chiffre = "digit", "figure", "number", chiffrer = "to calculate or compute", chiffré = "encrypted". Today, the word in Arabic is still ṣifr, and cognates of ṣifr are common in the languages of Europe and southwest Asia.