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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==

* [[Cartesian product]]

* [[Cartesian product]]

* [[Inverse relation]]

* [[Inverse relation]]

* [[Projection (set theory)]]

* [[Projection (mathematics)]]

* [[Relation (mathematics)]]

* [[Relation (mathematics)]]

* [[Relation composition]]

* [[Relation composition]]

[[Category:Logic]]

[[Category:Logic]]

[[Category:Mathematics]]

[[Category:Mathematics]]