Skip to main content Skip to Search Box

Definition: irrational number from Philip's Encyclopedia

In mathematics, any number that cannot be expressed as the ratio of two integers. An example is √2: like other irrational numbers, its expression as a decimal is infinite and non-repeating. Irrational numbers, together with the rational numbers, make up the set of real numbers.


Summary Article: irrational number from The Penguin Dictionary of Mathematics

A number that cannot be written as an integer or as a quotient of two integers. The real irrational numbers are infinite, nonrepeating decimals. Every complex number with a nonzero imaginary part is irrational.

There are two types of irrational number. Algebraic irrational numbers are irrational numbers that are roots of polynomial equations with rational coefficients; an example is √5(2.2360…), which is a root of x2 - 5 =0.

Transcendental numbers are irrational numbers that are not roots of polynomial equations with rational coefficients; π and e are transcendental numbers. Compare rational number; see also Dedekind cut; real number.

Copyright © Penguin Books Ltd, 1989, 1998, 2003, 2008

Related Credo Articles

Full text Article irrational number
Greenwood Dictionary of Education

A real number that cannot be expressed as a fraction. ( kgh ) ...

Full text Article III.41 Irrational and Transcendental Numbers
The Princeton Companion to Mathematics

An irrational number is one that cannot be written as a/b with both a and b integers. A great many naturally occurring numbers, such as ...

Full text Article Dedekind cut
Academic Press Dictionary of Science and Technology

A division of the elements of the number line or, more generally, an ordered field F into two nonempty disjoint subsets, A and B , such...

See more from Credo