setname1 http://www.openmath.org/cd/setname1.ocd 2003-04-01 2001-03-12 2 0 official alg1 arith1 logic1 quant1 relation1 set1 nums1 This CD defines common sets of mathematics Written by J.H. Davenport on 1999-04-18. Revised to add Zm, GFp, GFpn on 1999-11-09. Revised to add QuotientField and A on 1999-11-19. P This symbol represents the set of positive prime numbers. for all n | n is a positive prime number is equivalent to: n is a natural number and n > 1 and ((n=a*b and a and b are natural numbers) implies ((a=1 and b=n) or (b=1 and a=n))) N This symbol represents the set of natural numbers (including zero). for all n | n in the natural numbers is equivalent to saying n=0 or n-1 is a natural number Z This symbol represents the set of integers, positive, negative and zero. for all z | the statements z is an integer and z is a natural number or -z is a natural number are equivalent Q This symbol represents the set of rational numbers. for all z where z is a rational, there exists integers p and q with q > 1 and p/q = z for all a,b | a,b rational with a<b implies there exists rational a,c s.t. a<c and c<b R This symbol represents the set of real numbers. S \subset R and exists y in R : forall x in S x <= y) implies exists z in R such that (( forall x in S x <= z) and ((forall x in S x <= w) implies z <= w) C This symbol represents the set of complex numbers. for all z | if z is complex then there exist reals x,y s.t. z = x + i * y