This document is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
The copyright holder grants you permission to redistribute this
document freely as a verbatim copy. Furthermore, the copyright
holder permits you to develop any derived work from this document
provided that the following conditions are met.
a) The derived work acknowledges the fact that it is derived from
this document, and maintains a prominent reference in the
work to the original source.
b) The fact that the derived work is not the original OpenMath
document is stated prominently in the derived work. Moreover if
both this document and the derived work are Content Dictionaries
then the derived work must include a different CDName element,
chosen so that it cannot be confused with any works adopted by
the OpenMath Society. In particular, if there is a Content
Dictionary Group whose name is, for example, `math' containing
Content Dictionaries named `math1', `math2' etc., then you should
not name a derived Content Dictionary `mathN' where N is an integer.
However you are free to name it `private_mathN' or some such. This
is because the names `mathN' may be used by the OpenMath Society
for future extensions.
c) The derived work is distributed under terms that allow the
compilation of derived works, but keep paragraphs a) and b)
intact. The simplest way to do this is to distribute the derived
work under the OpenMath license, but this is not a requirement.
If you have questions about this license please contact the OpenMath
society at http://www.openmath.org.
setname1
http://www.openmath.org/cd
http://www.openmath.org/cd/setname1.ocd
2006-03-30
2004-03-30
3
1
Author: OpenMath Consortium
SourceURL: https://github.com/OpenMath/CDs
official
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
constant
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
constant
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
constant
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
constant
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
constant
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
constant
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