# algebraic number

A real number is an **algebraic number** if it is
a zero of a polynomial with integer coefficients;
and its degree is the least of the degrees of the
polynomials with it as a zero. For example, the rational number *a*/*b* (with *a*, *b* and non-zero integers) is an algebraic number of degree one, because it is a zero of
*bx*-*a*. The square root of two is an
algebraic number of degree two because it is a zero of
*x*^{2}-2.

If a real number is not algebraic, then it is a
**transcendental number**.
The base of the natural
logarithms *e* (2.71828...), and π (3.14159....) are both
transcendental. In fact, almost all real numbers are transcendental because the set of algebraic numbers is countable.

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