Real variable - Definition

In mathematics, a function of a real variable was the classical object of study in mathematical analysis of the nineteenth century, taking real numbers to real numbers. In contemporary terms it is a mathematical function F with function domain the real line, or possibly some subset of the real line such as an interval, and function codomain the real numbers. The distinction was usually from the function of a complex variable.

This concept is therefore more restrictive than simply a function accepting a real number; it is supposed to return a real number. In practice the classical theory also admitted complex number-valued functions, of great convenience in many fields such as Fourier analysis; this convention is continued in most parts of real analysis. The division of mathematical analysis into real variable and complex variable became obsolescent with the introduction of functional analysis from about 1920 onwards.