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Partial function

Set

Let

context $X,Y$

be sets. Then

definiendum $ f\in\text{PartialFunction}(X,Y) $

if

context $ f \in \text{Rel}(X,Y) $
postulate $ \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

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