Editing Function of a real variable (section)

=== Domain ===

The [[Domain of a function|domain]] of a function of several real variables is a subset of <math>\mathbb{R}</math> that is sometimes explicitly defined. In fact, if one restricts the domain ''X'' of a function ''f'' to a subset ''Y'' ⊂ ''X'', one gets formally a different function, the ''restriction'' of ''f'' to ''Y'', which is denoted ''f''<sub>|''Y''</sub>. In practice, it is often not harmful to identify ''f'' and ''f''<sub>|''Y''</sub>, and to omit the subscript <sub>|''Y''</sub>.

Conversely, it is sometimes possible to enlarge naturally the domain of a given function, for example by [[continuous function|continuity]] or by [[analytic continuation]]. This means that it is not worthy to explicitly define the domain of a function of a real variable.