Difference between revisions of "Tacit extension"
MyWikiBiz, Author Your Legacy — Friday November 22, 2024
Jump to navigationJump to searchJon Awbrey (talk | contribs) (copy text from [http://www.opencycle.net/ OpenCycle] of which Jon Awbrey is the sole author) |
Jon Awbrey (talk | contribs) (augment) |
||
| Line 1: | Line 1: | ||
| − | In [[logic]] and [[mathematics]], a '''tacit extension''' is | + | 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== | ||
| Line 5: | Line 5: | ||
* [[Cartesian product]] | * [[Cartesian product]] | ||
* [[Inverse relation]] | * [[Inverse relation]] | ||
| − | * [[Projection ( | + | * [[Projection (mathematics)]] |
* [[Relation (mathematics)]] | * [[Relation (mathematics)]] | ||
* [[Relation composition]] | * [[Relation composition]] | ||
| Line 14: | Line 14: | ||
[[Category:Logic]] | [[Category:Logic]] | ||
[[Category:Mathematics]] | [[Category:Mathematics]] | ||
| + | [[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.
