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Both sides previous revision Previous revision Next revision | Previous revision Last revision Both sides next revision | ||
partial_function [2013/12/29 22:20] nikolaj |
partial_function [2014/03/21 11:11] 127.0.0.1 external edit |
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==== Set ==== | ==== Set ==== | ||
Let | Let | ||
- | | @#88DDEE: $X,Y$ | | + | | @#55CCEE: context | @#55CCEE: $X,Y$ | |
be sets. Then | be sets. Then | ||
- | | @#FFBB00: $ f\in\text{PartialFunction}(X,Y) $ | | + | | @#FFBB00: definiendum | @#FFBB00: $ f\in\text{PartialFunction}(X,Y) $ | |
if | if | ||
- | | @#88DDEE: $ f \in \text{Rel}(X,Y) $ | | + | | @#55CCEE: context | @#55CCEE: $ f \in \text{Rel}(X,Y) $ | |
- | | @#55EE55: $ \langle x,a\rangle\in f \land \langle x,b\rangle\in f \Rightarrow a=b $ | | + | | @#55EE55: postulate | @#55EE55: $ \langle x,a\rangle\in f \land \langle x,b\rangle\in f \Rightarrow a=b $ | |
==== Discussion ==== | ==== Discussion ==== | ||
- | This is the same as | + | The definition can be written as |
$\{\langle x,a\rangle,\langle x,b\rangle\}\subseteq f \Rightarrow a=b.$ | $\{\langle x,a\rangle,\langle x,b\rangle\}\subseteq f \Rightarrow a=b.$ | ||
- | The definition 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]] |