Definition. Total & Partial function [003w]

Given a function \(f : A \to B\) we say that:

• The function is partial if there exists at least one \(a \in A\) such that \(f(a)\) is undefined. Commonly this is also denoted using the notation: \[ f : A \rightharpoonup B \]
• The function is total if for every \(a \in A\), \(f(a)\) is defined. This is commonly denoted using the notation: \[ f : A \to B \]