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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 = b''), but if ''c'' is equal to ''d'' (''c = d'') it does not necessarily hold that ''c'' is related to ''d'' (''cRd''). |
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| | In [[mathematical notation]], this is: |
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| | :<math>\forall a, b \in X,\ a R b \Rightarrow \; a = b.</math> |
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| | The [[identity relation]] is coreflexive by definition. Any relation that is coreflexive is thus a subset of the identity relation. |
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| | 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, 1), (3, 3), ...} but does not hold over {(2, 2), (4, 4), ...}. |
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| | ==Notes== |
| | <references /> |
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| | [[Category:Mathematical relations]] |
Revision as of 11:34, 20 January 2014
In mathematics, a coreflexive relation is a binary relation that is a subset of the identity relation.[1] Thus if a is related to b (aRb) then a is equal to b (a = b), but if c is equal to d (c = d) it does not necessarily hold that c is related to d (cRd).
In mathematical notation, this is:
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, 1), (3, 3), ...} but does not hold over {(2, 2), (4, 4), ...}.
Notes
- ↑ 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).