Let \(X\) and \(Y\) be sets. A function is a relation \(f\subseteq X\times Y\) with the property for all \(x\in X\) there is exactly one \(y\in Y\) with \((x,y)\in f\). We call \(X\) domain and \(Y\) codomain. We may write \(f\colon X\to Y\). Functions are also called map.