Differences
This shows you the differences between two versions of the page.
|
injective_function [2014/02/08 02:42] nikolaj |
injective_function [2014/03/21 11:11] |
||
|---|---|---|---|
| Line 1: | Line 1: | ||
| - | ===== Injective function ===== | ||
| - | ==== Set ==== | ||
| - | | @#88DDEE: $X,Y$ | | ||
| - | |||
| - | | @#FFBB00: $ f\in \mathrm{Injective}(X,Y)$ | | ||
| - | |||
| - | | @#88DDEE: $ f:X\to Y $ | | ||
| - | |||
| - | | @#55EE55: $ f(x)=f(y) \implies x=y $ | | ||
| - | |||
| - | ==== Discussion ==== | ||
| - | === Predicates === | ||
| - | | @#EEEE55: $Y$ ...countably infinite $\equiv (\mathrm{Injective}(\mathbb N,Y)\ne\emptyset) $ | | ||
| - | | @#EEEE55: $Y$ ... countable $\equiv$ ($Y$ ...finite) $\lor$ ($Y$ ...countably infinite) | | ||
| - | ==== Parents ==== | ||
| - | === Requirements === | ||
| - | [[Function]] | ||
