Difference between revisions of "Tacit extension"

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(copy text from [http://www.opencycle.net/ OpenCycle] of which Jon Awbrey is the sole author)
 
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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]].
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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==
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* [[Cartesian product]]
 
* [[Cartesian product]]
 
* [[Inverse relation]]
 
* [[Inverse relation]]
* [[Projection (set theory)]]
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* [[Projection (mathematics)]]
 
* [[Relation (mathematics)]]
 
* [[Relation (mathematics)]]
 
* [[Relation composition]]
 
* [[Relation composition]]
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[[Category:Logic]]
 
[[Category:Logic]]
 
[[Category:Mathematics]]
 
[[Category:Mathematics]]
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[[Category:Set Theory]]

Revision as of 13:40, 23 February 2009

In logic and mathematics, a tacit extension is an 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 operations to the 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