A joke in approximating numbers raised to irrational powers

One interesting result implies that numbers like 3^(sqrt(3)) will be transcendental (ie no polynomial will evaluate them to 0).

https://en.wikipedia.org/wiki/Gelfond%E2%80%93Schneider_theo...

No polynomial with rational coefficients. Of course x-y evaluates to 0 when x=y, even if y is a transcendental number.

Small but important correction: no polynomial with integer coefficients (equivalently, rational coefficients). p(x) = (x - 3^(sqrt(3))) is a perfectly fine polynomial with real coefficients.

Yes, I should have mentioned polynomials with rational coefficients(or indeed any algebraic numbers as coefficients due to transitivity of being algebraic).