Differences
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| Both sides previous revision Previous revision Next revision | Previous revision | ||
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pre-image [2013/09/06 22:04] 127.0.0.1 external edit |
pre-image [2014/03/21 11:11] (current) |
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| ===== Pre-image ===== | ===== Pre-image ===== | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| Pre-image of the function $f$ w.r.t the codomain subset $Z$. | Pre-image of the function $f$ w.r.t the codomain subset $Z$. | ||
| - | | @#88DDEE: $ Z $ | | + | | @#55CCEE: context | @#55CCEE: $ Z $ | |
| - | | @#88DDEE: $ f\in X^Y $ | | + | | @#55CCEE: context | @#55CCEE: $ f\in X^Y $ | |
| - | | @#55EE55: $ x\in f^{-1}(Y) $ | | + | | @#55EE55: postulate | @#55EE55: $ x\in f^{-1}(Y) $ | |
| - | | @#55EE55: $ f(x)\in Z $ | | + | | @#55EE55: postulate | @#55EE55: $ f(x)\in Z $ | |
| ==== Ramifications ==== | ==== Ramifications ==== | ||
| === Reference === | === Reference === | ||
| - | Mizar files: [[http://mizar.org/JFM/Vol1/funct_1.html|FUNCT_1]] | ||
| - | |||
| Wikipedia: [[http://en.wikipedia.org/wiki/Image_%28mathematics%29|Image]] | Wikipedia: [[http://en.wikipedia.org/wiki/Image_%28mathematics%29|Image]] | ||
| - | |||
| ==== Parents ==== | ==== Parents ==== | ||
| - | Set constructor | ||
| === Context === | === Context === | ||
| [[Function]] | [[Function]] | ||
