Transcendental number
Analysis
A real or complex number that is not a root of any nonzero polynomial with rational coefficients.
What is usually left out
Almost every real number is transcendental, because the algebraic numbers are countable and the reals are not. Proving any specific number transcendental is nonetheless difficult: π and e are known to be, while whether π + e is transcendental — or even irrational — is open.