### Topic Page: Irrational numbers

**irrational number**from

*Philip's Encyclopedia*

**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 x^{2} - 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.

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