Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision Next revision | Previous revision Next revision Both sides next revision | ||
|
injective_function [2013/05/20 13:31] nikolaj |
injective_function [2014/02/08 02:42] nikolaj |
||
|---|---|---|---|
| Line 1: | Line 1: | ||
| ===== Injective function ===== | ===== Injective function ===== | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| - | | $X,Y$ | | + | | @#88DDEE: $X,Y$ | |
| - | ^ $ f\in Y^X_\text{inj} $ ^ | + | | @#FFBB00: $ f\in \mathrm{Injective}(X,Y)$ | |
| - | | $ f:X\to Y $ | | + | | @#88DDEE: $ f:X\to Y $ | |
| - | ^ $ f(x)=f(y) \implies x=y $ ^ | + | | @#55EE55: $ f(x)=f(y) \implies x=y $ | |
| - | ==== Ramifications ==== | + | ==== Discussion ==== |
| - | === Discussion === | + | === Predicates === |
| - | + | | @#EEEE55: $Y$ ...countably infinite $\equiv (\mathrm{Injective}(\mathbb N,Y)\ne\emptyset) $ | | |
| - | >Mizar actually defines injective functions more general: They define it more early and it's a refinement of the general function predicate, which is to say that they don't require that one needs to specify $X,Y$. | + | | @#EEEE55: $Y$ ... countable $\equiv$ ($Y$ ...finite) $\lor$ ($Y$ ...countably infinite) | |
| - | + | ==== Parents ==== | |
| - | === Reference === | + | === Requirements === |
| - | Mizar files: [[http://mizar.org/JFM/Vol1/funct_1.html|FUNCT_1]] | + | |
| - | + | ||
| - | Wikipedia: [[http://en.wikipedia.org/wiki/Injective_function|Injective function]] | + | |
| - | + | ||
| - | ==== Context ==== | + | |
| - | === Parents === | + | |
| [[Function]] | [[Function]] | ||
