Difference between revisions of "Tacit extension"
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| − | 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== | ||
| + | {{col-begin}} | ||
| + | {{col-break}} | ||
* [[Cartesian product]] | * [[Cartesian product]] | ||
* [[Inverse relation]] | * [[Inverse relation]] | ||
| − | * [[Projection ( | + | * [[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]] | ||
Latest revision as of 13:28, 3 May 2019
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
Template:Col-breakTemplate:Col-breakTemplate:Col-endDocument 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.
