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bijective_function [2014/02/08 02:46] nikolaj |
bijective_function [2014/02/08 18:39] nikolaj |
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| ===== Bijective function ===== | ===== Bijective function ===== | ||
| ==== Set ==== | ==== Set ==== | ||
| - | | @#88DDEE: $X,Y$ | | + | | @#88DDEE: $X,Y$ ... set | |
| | @#FFBB00: $ f\in \mathrm{Bijective}(X,Y) $ | | | @#FFBB00: $ f\in \mathrm{Bijective}(X,Y) $ | | ||
| - | | @#88DDEE: $ f\in \mathrm{Injective}(X,Y) $ | | + | | @#AAFFAA: $ f\in \mathrm{Injective}(X,Y) $ | |
| - | | @#88DDEE: $ f\in \mathrm{Surjective}(X,Y) $| | + | | @#AAFFAA: $ f\in \mathrm{Surjective}(X,Y) $| |
| ==== Discussion ==== | ==== Discussion ==== | ||
| Line 15: | Line 15: | ||
| We also write $X$ smaller $Y$. | We also write $X$ smaller $Y$. | ||
| - | | @#EEEE55: $Y...\mathrm{countably\ infinite}\equiv \mathbb N\approx Y$ | | + | | @#EEEE55: $Y$ ... countably infinite $\equiv \mathbb N\approx Y$ | |
| ==== Parents ==== | ==== Parents ==== | ||
| === Requirements === | === Requirements === | ||
| [[Injective function]], [[Surjective function]] | [[Injective function]], [[Surjective function]] | ||
