A function from $A$ to $B$ is a relation $f$ from $A$ to $B$ such that both of the following hold:

1. $\text{Dom}(f)=A=\text{Domain space}(f)$
2. If $(x,y)\in f$ and $(x,z)\in f$, then $y=z$.

We denote the phrase "$f$ is a function from $A$ to $B$" with the notation $f:A\to B$.

• If $B=A$, we say that $f$ is a function on $A$.