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partial_function [2013/12/29 22:20] nikolaj |
partial_function [2014/04/01 16:25] nikolaj |
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| ===== Partial function ===== | ===== Partial function ===== | ||
| ==== Set ==== | ==== Set ==== | ||
| - | Let | + | | @#55CCEE: context | @#55CCEE: $X,Y$ | |
| - | | @#88DDEE: $X,Y$ | | + | | @#FFBB00: definiendum | @#FFBB00: $ f\in\text{PartialFunction}(X,Y) $ | |
| - | be sets. Then | + | | @#55CCEE: context | @#55CCEE: $ f \in \text{Rel}(X,Y) $ | |
| - | | @#FFBB00: $ f\in\text{PartialFunction}(X,Y) $ | | + | | @#55EE55: postulate | @#55EE55: $ \langle x,a\rangle\in f \land \langle x,b\rangle\in f \Rightarrow a=b $ | |
| - | if | + | |
| - | | @#88DDEE: $ f \in \text{Rel}(X,Y) $ | | + | |
| - | | @#55EE55: $ \langle x,a\rangle\in f \land \langle x,b\rangle\in f \Rightarrow a=b $ | | + | |
| ==== Discussion ==== | ==== Discussion ==== | ||
| Line 16: | Line 13: | ||
| It says that each argument $x$ for the function can result in only one value. (functionality) | It says that each argument $x$ for the function can result in only one value. (functionality) | ||
| === Reference === | === Reference === | ||
| - | Mizar files: | ||
| - | [[http://mizar.org/JFM/Vol1/funct_1.html|FUNC_1]], | ||
| - | [[http://markun.cs.shinshu-u.ac.jp/mirror/mizar/JFM/Vol1/partfun1.html|PARTFUN1]] | ||
| - | |||
| Wikipedia: | Wikipedia: | ||
| [[http://en.wikipedia.org/wiki/Partial_function|Partial function]] | [[http://en.wikipedia.org/wiki/Partial_function|Partial function]] | ||
