Relation

A relation \(\mathbb{R}\) from \(A\) to \(B\) is a subset of \(A\times B\).

A relation \(\mathbb{R}\) from \(A\) to \(A\) is also called a relation on \(A\).

A knowledge-base/docs/Public/Math/Sets/function from \(A\) to \(B\) is a relation \(f\) from \(A\) to \(B\) such that: - the [[domain]] of \(f\) is \(A\) - if \((x,y) \in f\) and \((x, z) \in f\), then \(y=z\)

We write \(f: A \implies B\) and read: - "f is a function from A to B"