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In [[logic]] and [[mathematics]], a '''tacit extension''' is in formal respects the simplest or the logically least committal of the several possible [[set]] [[operator|operation]]s that are [[inverse relation|inverse]] to the [[set theory|set-theoretic]] operation of [[projection (set theory)|projection]].
In [[logic]] and [[mathematics]], a '''tacit extension''' is an [[injection (mathematics)|injection]] of a [[set]] into a [[cartesian product]] that has that set as one of its factors. There are many such injections, all of which serve as [[inverse]] [[operation]]s to the [[projection (mathematics)|projection]] of the Cartesian product onto the set in question, but the tacit extension is the one that places no additional constraints on the injection mapping.
==See also==
==See also==
{{col-begin}}
{{col-break}}
* [[Cartesian product]]
* [[Cartesian product]]
* [[Inverse relation]]
* [[Inverse relation]]
* [[Projection (set theory)]]
* [[Injection (mathematics)]]
* [[Projection (mathematics)]]
{{col-break}}
* [[Relation (mathematics)]]
* [[Relation (mathematics)]]
* [[Relation composition]]
* [[Relation composition]]
* [[Relation construction]]
* [[Relation construction]]
* [[Relation reduction]]
* [[Relation reduction]]
{{col-end}}
==Document history==
Portions of the above article were adapted from the following sources under the GNU Free Documentation License, under other applicable licenses, or by permission of the copyright holders.
* [http://mywikibiz.com/Tacit_extension Tacit Extension], [http://mywikibiz.com/ MyWikiBiz]
* [http://web.archive.org/web/20161118224624/https://planetmath.org/TacitExtension Tacit Extension], [https://planetmath.org/ PlanetMath]
* [http://web.archive.org/web/20060913000000/https://en.wikipedia.org/wiki/Tacit_extension Tacit Extension], [http://en.wikipedia.org/ Wikipedia]
[[Category:Category Theory]]
[[Category:Category Theory]]
[[Category:Logic]]
[[Category:Logic]]
[[Category:Mathematics]]
[[Category:Mathematics]]
[[Category:Relation Theory]]
[[Category:Set Theory]]
