HEADERS_END

A number which is not an algebraic number is called transcendental.

Transcendental numbers are a strict subset of the irrational numbers.

Although "almost all" real numbers are transcendental it is difficult

to prove that a given number that occurs naturally is transcendental.

The usual weapon of choice is the Gelfond-Schneider Theorem.

The size of the set of transcendental numbers is the size of the continuum c. (See Uncountable sets).

Some numbers shown to be transcendental are EQN:e , EQN:\pi , sin(1) , log(2) and EQN:e^\pi

Whether EQN:2^e , EQN:2^\pi or EQN:\pi^e are transcendental or not has still to be decided.