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relation_domain [2013/08/23 21:52] nikolaj |
relation_domain [2014/07/11 20:38] nikolaj |
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| ===== Relation domain ===== | ===== Relation domain ===== | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| - | Let | + | | @#55CCEE: context | @#55CCEE: $ R $ | |
| - | | @#88DDEE: $ R $ | | + | |
| - | be a set with | + | |
| | $ c\in R $ | | | $ c\in R $ | | ||
| - | | @#55EE55: $ \forall c.\ \exists a,b.\ c=\langle a,b\rangle $ | | + | | @#55EE55: postulate | @#55EE55: $ \forall c.\ \exists a,b.\ c=\langle a,b\rangle $ | |
| - | Then | + | | @#FFBB00: definiendum | @#FFBB00: $ x\in \mathrm{dom}(R) $ | |
| - | | @#FFBB00: $ x\in \mathrm{dom}(R) $ | | + | | @#55EE55: postulate | @#55EE55: $ \exists y.\ \langle x,y \rangle\in R $ | |
| - | if | + | |
| - | | @#55EE55: $ \exists y.\ \langle x,y \rangle\in R $ | | + | |
| ==== Discussion ==== | ==== Discussion ==== | ||
| === Reference === | === Reference === | ||
| Wikipedia: [[http://en.wikipedia.org/wiki/Domain_of_a_function|Domain of a function]] | Wikipedia: [[http://en.wikipedia.org/wiki/Domain_of_a_function|Domain of a function]] | ||
| - | ==== Context ==== | + | ==== Parents ==== |
| - | === Requirements === | + | === Context === |
| [[Ordered pair]] | [[Ordered pair]] | ||
