
Glossary: Prime Pages: Top 5000: 
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 nonzero
integers) is
an algebraic number of degree one, because it is a zero of
bxa. 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 pi (3.14159....) are both transcendental. In fact, almost all real numbers are transcendental because the set of algebraic numbers is countable.
Chris K. Caldwell © 19992018 (all rights reserved)
