To make things more complex, the same function can have transcendental/algebraic number
answers depending on the domain
. For example, sin
) is transcendental, while sin
) 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