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| ===== Binary relation ===== | ===== Binary relation ===== | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| - | | @#88DDEE: $X,Y$ | | + | | @#55CCEE: context | @#55CCEE: $X,Y$ | |
| - | | @#FFBB00: $ \text{Rel}(X,Y) \equiv \mathcal{P}(X\times Y) $ | | + | | @#FFBB00: definiendum | @#FFBB00: $ \text{Rel}(X,Y) \equiv \mathcal{P}(X\times Y) $ | |
| The set of all binary relations on $X\times Y$. | The set of all binary relations on $X\times Y$. | ||
| ==== Discussion ==== | ==== Discussion ==== | ||
| - | If | + | If $R$ is a binary relation, we write $x R y\equiv \langle x,y\rangle \in R$ |
| - | | @#88DDEE: $R$ | | + | |
| - | is a binary relation, we write | + | |
| - | | @#EEEE55: $x R y\equiv \langle x,y\rangle \in R$ | | + | |
| - | === Reference === | + | |
| - | Mizar files: [[http://markun.cs.shinshu-u.ac.jp/mirror/mizar/JFM/Vol1/relat_1.html|RELAT_1]] | + | |
| + | === Reference === | ||
| Wikipedia: [[http://en.wikipedia.org/wiki/Binary_relation|Binary relation]] | Wikipedia: [[http://en.wikipedia.org/wiki/Binary_relation|Binary relation]] | ||
| ==== Parents ==== | ==== Parents ==== | ||
| - | === Requirements === | + | === Context === |
| [[Cartesian product]], [[Power set]] | [[Cartesian product]], [[Power set]] | ||
