Domain - Knowlpedia

A domain is the set of inputs of a function: if $f:A\to B$ is a function, then its domain is the set $A$ .

Remarks

Changing the domain (for example by taking a restriction) produces a new function, even if the output rule looks the same. The elements of the domain appear as the first components of ordered pairs in the graph of $f$ .

Examples

For $f:\mathbb{R}\to\mathbb{R}$ defined by $f(x)=x^2$ , the domain is $\mathbb{R}$ (the real numbers).
For the inclusion map $i:S\to A$ with $S\subseteq A$ , the domain is $S$ .