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bijective_function [2014/02/08 02:47] nikolaj |
bijective_function [2014/03/21 11:11] 127.0.0.1 external edit |
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| ===== Bijective function ===== | ===== Bijective function ===== | ||
| ==== Set ==== | ==== Set ==== | ||
| - | | @#88DDEE: $X,Y$ | | + | | @#55CCEE: context | @#55CCEE: $X,Y$ ... set | |
| - | | @#FFBB00: $ f\in \mathrm{Bijective}(X,Y) $ | | + | | @#FFBB00: definiendum | @#FFBB00: $ f\in \mathrm{Bijective}(X,Y) $ | |
| - | | @#88DDEE: $ f\in \mathrm{Injective}(X,Y) $ | | + | | @#AAFFAA: inclusion | @#AAFFAA: $ f\in \mathrm{Injective}(X,Y) $ | |
| - | | @#88DDEE: $ f\in \mathrm{Surjective}(X,Y) $| | + | | @#AAFFAA: inclusion | @#AAFFAA: $ f\in \mathrm{Surjective}(X,Y) $| |
| ==== Discussion ==== | ==== Discussion ==== | ||
| === Predicates === | === Predicates === | ||
| - | | @#EEEE55: $X\approx Y\equiv \mathrm{Bijective}(X,Y)\ne\emptyset$ | | + | | @#EEEE55: predicate | @#EEEE55: $X\approx Y\equiv \mathrm{Bijective}(X,Y)\ne\emptyset$ | |
| We also write $X$ equinumerous $Y$. | We also write $X$ equinumerous $Y$. | ||
| - | | @#EEEE55: $X\preccurlyeq Y \equiv \exists (X'\subseteq Y).\ X'\approx X$ | | + | | @#EEEE55: predicate | @#EEEE55: $X\preccurlyeq Y \equiv \exists (X'\subseteq Y).\ X'\approx X$ | |
| We also write $X$ smaller $Y$. | We also write $X$ smaller $Y$. | ||
| - | | @#EEEE55: $Y$ ... countably infinite $\equiv \mathbb N\approx Y$ | | + | | @#EEEE55: predicate | @#EEEE55: $Y$ ... countably infinite $\equiv \mathbb N\approx Y$ | |
| ==== Parents ==== | ==== Parents ==== | ||
| - | === Requirements === | + | === Context === |
| [[Injective function]], [[Surjective function]] | [[Injective function]], [[Surjective function]] | ||
