irrational number

A real number is an irrational number if it is not a rational number.  Common examples include the square root of two, the base of the natural logarithms e, and pi (3.14159....).  The decimal expansion of irrational numbers do not repeat (in equal length blocks), though they can have a simple pattern such as

0.101001000100001000001... or
0.123456789101112131415...

Almost all real numbers are irrational; so if you were to pick a real number "at random," then the "probability" that it is irrational is one.  (Technically, the set of rational numbers is countable, so the Lebesgue measure of the set of irrational numbers in [a,b] is b-a.)

See Also: RationalNumber, AlgebraicNumber