nums1 http://www.openmath.org/cd/nums1.ocd 2003-04-01 2001-03-12 2 0 official alg1 arith1 relation1 logic1 transc1 setname1 set1 interval1 fns1 integer1 limit1 This CD is intended to be `compatible' with the MathML view of constructors for numbers (integers to an arbitrary base, rationals) and symbols for some common numerical constants. This CD holds a set of symbols for creating numbers, including some defined constants (i.e. nullary constructors). based_integer This symbol represents the constructor function for integers, specifying the base. It takes two arguments, the first is a positive integer to denote the base to which the number is represented, the second argument is a string which contains an optional sign and the digits of the integer, using 0-9a-z (as a consequence of this no radix greater than 35 is supported). Base 16 and base 10 are already covered in the encodings of integers. A representation of 8 (radix 10) base 8 8 8 10 rational This symbol represents the constructor function for rational numbers. It takes two arguments, the first is an integer p to denote the numerator and the second a nonzero integer q to denote the denominator of the rational p/q. A representation of the rational number 1/2 1 2 infinity A symbol to represent the notion of infinity. if x is a real number then x < infinity e This symbol represents the base of the natural logarithm, approximately 2.718. See Abramowitz and Stegun, Handbook of Mathematical Functions, section 4.1. e = the sum as j ranges from 0 to infinity of 1/(j!) 2.718 = The decimal approximation to 3 significant places of e i This symbol represents the square root of -1. i^2 = -1 2 pi A symbol to convey the notion of pi, approximately 3.142. The ratio of the circumference of a circle to its diameter. pi = 4 * the sum as j ranges from 0 to infinity of ((1/(4j+1))-(1/(4j+3))) 4 4 4 3 3.142 = The decimal approximation to 3 significant places of pi gamma A symbol to convey the notion of the gamma constant as defined in Abramowitz and Stegun, Handbook of Mathematical Functions, section 6.1.3. It is the limit of 1 + 1/2 + 1/3 + ... + 1/m - ln m as m tends to infinity, this is approximately 0.5772 15664. gamma = limit_(m -> infinity)(sum_(j ranges from 1 to m)(1/j) - ln m) 1 0.577 = The decimal approximation to 3 significant places of gamma NaN A symbol to convey the notion of not-a-number. The result of an ill-posed floating computation. See IEEE standard for floating point representations. NaN is not equal to NaN