# OpenMath Content Dictionary: quant1

Canonical URL:
http://www.openmath.org/cd/quant1.ocd
CD Base:
http://www.openmath.org/cd
CD File:
quant1.ocd
CD as XML Encoded OpenMath:
quant1.omcd
Defines:
exists, forall
Date:
2004-05-11
Version:
3 (Revision 2)
Review Date:
2006-03-30
Status:
official


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.
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.
society at http://www.openmath.org.

  Author: OpenMath Consortium
SourceURL: https://github.com/OpenMath/CDs


This CD holds the definitions of the basic universal ("for all") quantifier and existential ("there exists") quantifier. It is intended to be `compatible' with the MathML elements representing these quantifiers.

## forall

Role:
binder
Description:

This symbol represents the universal ("for all") quantifier which takes two arguments. It must be placed within an OMBIND element. The first argument is the bound variables (placed within an OMBVAR element), and the second is an expression.

Example:
An example to represent the statement for all real x, |sin(x)| <= 1
$\forall x.x\in \mathbb{R}⇒|\mathrm{sin}\left(x\right)|\le 1.0$
Signatures:
sts

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## exists

Role:
binder
Description:

This symbol represents the existential ("there exists") quantifier which takes two arguments. It must be placed within an OMBIND element. The first argument is the bound variables (placed within an OMBVAR element), and the second is an expression.

Example:
An example which represents the statement that there is no solution to x^n+y^n=z^n for n>2, that is: it is not true that there exists x,y,z,n | n>2 and x^n+y^n=z^n
$¬\exists x,y,z,n.x\in \mathbb{Z}\wedge y\in \mathbb{Z}\wedge z\in \mathbb{Z}\wedge n\in \mathbb{Z}\wedge n>2\wedge {x}^{n}+{y}^{n}={z}^{n}$
Signatures:
sts

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