Transcendental number definition query

Question

The wiki page says that a transcendental number is defined as "a number that is not the root of a non-zero polynomial with rational coefficients". When they provide this definition, shouldn't they add that the polynomial order has to be finite also?

Answer 1

Any polynomial is by definition of finite order, so it’s not necessary to include it in the definition. If it has infinite order, then it is a Taylor series or something similar, and not a polynomial.