Real functions

In mathematics, a function of a real variable is a function whose domain is a subset of ${\displaystyle \mathbb {R} }$. Many real functions that are often encountered have their domain contain an interval of non-empty interior, and may be continuous, or have some degree of smoothness, over one or more intervals, each of non-empty interior, in the domain. In older texts, the theory of functions of a real variable is often synonymous with what is usually now called real analysis.