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Partial function
Set
Let
$X,Y$ |
be sets. Then
$ f\in\text{PartialFunction}(X,Y) $ |
if
$ f \in \text{Rel}(X,Y) $ |
$ \langle x,a\rangle\in f \land \langle x,b\rangle\in f \Rightarrow a=b $ |
Discussion
The definition can be written as
$\{\langle x,a\rangle,\langle x,b\rangle\}\subseteq f \Rightarrow a=b.$
It says that each argument $x$ for the function can result in only one value. (functionality)
Reference
Wikipedia: Partial function