In mathematics, the real numbers may be described informally as numbers that can be given by an infinite decimal representation, such as 2.4871773339…. The real numbers include both rational numbers, such as 42 and −23/129, and irrational numbers, such as π and the square root of 2, and can be represented as points along an infinitely long number line.
A more rigorous definition of the real numbers was one of the most important developments of 19th century mathematics. Popular definitions in use today include equivalence classes of Cauchy sequences of rational numbers, Dedekind cuts, a more sophisticated version of "decimal representation", and an axiomatic definition of the real numbers as the unique complete Archimedean ordered field.
Real numbers are so called to distinguish them from "imaginary numbers" (what we now call "complex numbers").