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In [[mathematics]], a '''coreflexive relation''' is a [[binary relation]] that is a subset of the [[identity relation]].<ref>Fonseca de Oliveira, J. N., & Pereira Cunha Rodrigues, C. D. J. (2004). Transposing Relations: From Maybe Functions to Hash Tables. In Mathematics of Program Construction (p. 337).</ref> Thus if ''a'' is related to ''b'' (''aRb'') then ''a'' is equal to ''b'' (''a&nbsp;=&nbsp;b''), but if ''c'' is equal to ''d'' (''c&nbsp;=&nbsp;d'') it does not necessarily hold that ''c'' is related to&nbsp;''d''&nbsp;(''cRd'').
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In [[mathematical notation]], this is:
 
:<math>\forall a, b \in X,\ a R b \Rightarrow \; a = b.</math>
 
The [[identity relation]] is coreflexive by definition. Any relation that is coreflexive is thus a subset of the identity relation.
 
For example, consider the relation ''R'' as "equal to and odd".   Over the set of positive integers, the relationship ''R'' holds over the pairs {(1,&nbsp;1),&nbsp;(3,&nbsp;3),&nbsp;...} but does not hold over {(2,&nbsp;2),&nbsp;(4,&nbsp;4),&nbsp;...}.
 
==Notes==
<references />
 
[[Category:Mathematical relations]]

Latest revision as of 01:37, 11 December 2014

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