To make things more complex, the same function can have transcendental/

algebraic number answers depending on the

domain. For example,

sin (1

radian) is transcendental, while

sin (1

degree) is algebraic.

Since e is transcendental, ln a (where a is not equal to 0 or 1 and is algebraic) is also transcendental.

A fundamental problem about transcendental numbers that still needs to be proved is whether a^b, where a is not equal to 0 or 1 and is

algebraic and b is

algebraic but not

rational, is

*always* transcendental.