Domain

If $f\colon A\to B$ is a function , then the domain of $f$ is the input set $A$.

More generally, if $R\subseteq A\times B$ is a relation , its domain is the subset

where $A\times B$ is the Cartesian product .

Examples:

• For $f\colon\mathbb{R}\to\mathbb{R}$ defined by $f(x)=x^2$, the domain is $\mathbb{R}$.
• If $R=\{(1,a),(2,a)\}\subseteq\{1,2,3\}\times\{a,b\}$, then $\mathrm{dom}(R)=\{1,2\}$.