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algebraic number (another Prime Pages' Glossary entries) |
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Glossary:
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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
x2-2.
If a real number is not algebraic, then it is a transcendental number. The base of the natural logarithms e (2.71828...), and pi (3.14159....) are both transcendental. In fact, almost all real numbers are transcendental because the set of algebraic numbers is countable.
Chris Caldwell © 1999-2008 (all rights reserved)
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