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image [2013/05/20 00:01] nikolaj |
image [2013/09/06 22:04] 127.0.0.1 external edit |
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| ===== Image ===== | ===== Image ===== | ||
| ==== Definition ==== | ==== Definition ==== | ||
| - | | $ R $ | | + | | @#88DDEE: $ R\in \text{Rel}(X,Y) $ | |
| - | | $ \forall_R c\ \exists a,b\ (c=\langle a,b\rangle) $ | | + | | @#55EE55: $ y\in \mathrm{im}(R) $ | |
| - | >This is quite general. Might be that we can just restrict this to actual relations (the "smaller" set constructor) | + | | @#55EE55: $ \exists x\ (\langle x,y \rangle \in R) $ | |
| - | + | ||
| - | ^ $ y\in \mathrm{im}(R) $ ^ | + | |
| - | + | ||
| - | ^ $ \exists x\ (\langle x,y \rangle \in R) $ ^ | + | |
| ==== Ramifications ==== | ==== Ramifications ==== | ||
| Line 18: | Line 14: | ||
| Wikipedia: [[http://en.wikipedia.org/wiki/Image_%28mathematics%29|Image]] | Wikipedia: [[http://en.wikipedia.org/wiki/Image_%28mathematics%29|Image]] | ||
| - | ==== Context ==== | + | ==== Parents ==== |
| Set constructor | Set constructor | ||
| - | === Parents === | + | === Equivalent to === |
| - | [[Ordered pair]] | + | [[Binary relation]] |
