# Irrational number

In mathematics, an **irrational number** is any real number that is not a rational number, i.e., one that cannot be written as a ratio of two integers, i.e., it is not of the form

- [math]\Large \frac{a}{b}[/math]

where a and b are integers and b is not zero. It can readily be shown that the irrational numbers are precisely those numbers whose expansion in any given base (decimal, binary, etc) never ends and never enters a periodic pattern, but no mathematician takes that to be a definition. Some examples of irrational numbers are [math]\sqrt{2}[/math] or [math]e[/math].