Choosing a value of that satisfies both lemmas leads to a non-zero integer added to a vanishingly small quantity being equal to zero: an impossibility. It follows that the original assumption, that can satisfy a polynomial equation with integer coefficients, is also impossible; that is, is transcendental.
Choosing a value of that satisfies both lemmas leads to a non-zero integer added to a vanishingly small quantity being equal to zero an impossibility It follows that the original assumption that can satisfy a polynomial equation with integer coefficients, is also impossible; that is, is transcendental.