Definition:Partial function

A partial function is like a function, except that it does not need to give an output for every input. However, the outputs it does give must be unambiguous. One way to formalize this is by defining a partial function as a function from a restricted domain:

Definition: Partial function

A partial function [math]f : A \href{/cs2800/wiki/index.php/%E2%86%9B}{↛} B [/math] is a subset [math]S⊆A [/math] (called the support of [math]f [/math]), along with a function [math]\tilde{f}:S \href{/cs2800/wiki/index.php/%E2%86%92}{→}B [/math] We say that [math]f(x)=y [/math] if [math]\tilde{f}(x) = y [/math] and [math]f(x) [/math] is undefined if [math]x \href{/cs2800/wiki/index.php/%5Cnotin}{\notin} S [/math].