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injective_function [2013/05/20 13:31] nikolaj |
injective_function [2014/03/21 11:11] (current) |
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| ===== Injective function ===== | ===== Injective function ===== | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| - | | $X,Y$ | | + | | @#55CCEE: context | @#55CCEE: $X,Y$ | |
| - | ^ $ f\in Y^X_\text{inj} $ ^ | + | | @#FFBB00: definiendum | @#FFBB00: $ f\in \mathrm{Injective}(X,Y)$ | |
| - | | $ f:X\to Y $ | | + | | @#55CCEE: context | @#55CCEE: $ f:X\to Y $ | |
| - | ^ $ f(x)=f(y) \implies x=y $ ^ | + | | @#55EE55: postulate | @#55EE55: $ f(x)=f(y) \implies x=y $ | |
| - | ==== Ramifications ==== | + | ==== Discussion ==== |
| - | === Discussion === | + | ==== Parents ==== |
| - | + | === Context === | |
| - | >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 $X,Y$. | + | |
| - | + | ||
| - | === Reference === | + | |
| - | 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]] | ||
