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# OpenMath Content Dictionary: relation1

Canonical URL:
http://www.openmath.org/cd/relation1.ocd
CD Base:
http://www.openmath.org/cd
CD File:
relation1.ocd
CD as XML Encoded OpenMath:
relation1.omcd
Defines:
approx, eq, geq, gt, leq, lt, neq
Date:
2004-03-30
Version:
3
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.
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.
society at http://www.openmath.org.


This CD holds the common arithmetic relations. It is intended to be `compatible' with the appropriate MathML elements.

## eq

Role:
application
Description:

This symbol represents the binary equality function.

Commented Mathematical property (CMP):
a=b and b=c implies a=c
Formal Mathematical property (FMP):
$a=b\wedge b=c⇒a=c$
Example:
An example which represents the statement 1 + 2 = 3.
$1+2=3$
Signatures:
sts

 [Next: lt] [Last: approx] [Top]

## lt

Role:
application
Description:

This symbol represents the binary less than function which returns true if the first argument is less than the second, it returns false otherwise.

Commented Mathematical property (CMP):
a<b and b<c implies a<c
Formal Mathematical property (FMP):
$a
Example:
An example which represents the statement 1 + 2 < 4
$\left(1+2\right)<4$
Signatures:
sts

 [Next: gt] [Previous: eq] [Top]

## gt

Role:
application
Description:

This symbol represents the binary greater than function which returns true if the first argument is greater than the second, it returns false otherwise.

Commented Mathematical property (CMP):
a>b and b>c implies a>c
Formal Mathematical property (FMP):
$a>b\wedge b>c⇒a>c$
Example:
An example which represents the statement 1 + 2 > 2
$\left(1+2\right)>2$
Signatures:
sts

 [Next: neq] [Previous: lt] [Top]

## neq

Role:
application
Description:

This symbol represents the binary inequality function.

Commented Mathematical property (CMP):
it is not true that a=/b and b=/c implies a=/c
Formal Mathematical property (FMP):
$¬\left(a\ne b\wedge b\ne c⇒a\ne c\right)$
Example:
An example which represents the statement 1 + 2 not = 2
$1+2\ne 2$
Signatures:
sts

 [Next: leq] [Previous: gt] [Top]

## leq

Role:
application
Description:

This symbol represents the binary less than or equal to function which returns true if the first argument is less than or equal to the second, it returns false otherwise.

Commented Mathematical property (CMP):
a<=b and b<=c implies a<=c
Formal Mathematical property (FMP):
$a\le b\wedge b\le c⇒a\le c$
Example:
An example which represents the statement 1 + 2 <= 4
$1+2\le 4$
Signatures:
sts

 [Next: geq] [Previous: neq] [Top]

## geq

Role:
application
Description:

This symbol represents the binary greater than or equal to function which returns true if the first argument is greater than or equal to the second, it returns false otherwise.

Commented Mathematical property (CMP):
a>=b and b>=c implies a>=c
Formal Mathematical property (FMP):
$a\ge b\wedge b\ge c⇒a\ge c$
Example:
An example which represents the statement 1 + 2 >= 3
$1+2\ge 3$
Signatures:
sts

 [Next: approx] [Previous: leq] [Top]

## approx

Role:
application
Description:

This symbol is used to denote the approximate equality of its two arguments.

Example:
\pi is approximately 355/113
$\pi \approx \frac{355}{113}$
Signatures:
sts

 [First: eq] [Previous: geq] [Top]

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