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{{for|relations ''R'' where ''aRb'' or ''bRa'' for all ''a'' and ''b''|connected relation}} |
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In [[mathematics]], '''total relation''' may refer to: |
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In [[mathematics]], a total relation ''R'' is [[binary relation]] where the source set equals the domain {''x'' : there is a ''y'' with ''xRy'' }. Since a relation ''R'' ⊂ ''A'' x ''B'' is a set of [[ordered pair]]s, an arbitrary subset of ''A'' may be the domain of ''R''. But when f: ''A'' → ''B'' is a [[function (mathematics)|function]], the domain of f is all of ''A'', and f is a total relation. On the other hand, if f is a [[partial function]], then the domain may be a proper subset of ''A'', in which case f is not a total relation. |
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* [[Serial relation]] (a binary relation that relates every domain element to some range element), or |
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* [[Connected relation]] (a binary relation in which any two elements are comparable). |
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==References== |
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{{disambiguation}} |
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* [[Gunther Schmidt]] & Michael Winter (2018) ''Relational Topology'' |
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[[Category:Binary relations]] |
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Revision as of 03:14, 13 April 2022
In mathematics, a total relation R is binary relation where the source set equals the domain {x : there is a y with xRy }. Since a relation R ⊂ A x B is a set of ordered pairs, an arbitrary subset of A may be the domain of R. But when f: A → B is a function, the domain of f is all of A, and f is a total relation. On the other hand, if f is a partial function, then the domain may be a proper subset of A, in which case f is not a total relation.
References
- Gunther Schmidt & Michael Winter (2018) Relational Topology