Talk:Schanuel's Conjecture Implies Algebraic Independence of Pi and Euler's Number over the Rationals

Your objections
Re your first objection, I am failing to see how this definition cannot apply.

Let there be rational numbers $a$ and $b$ such that $a \times 1 + b \times \left({2 i \pi}\right) = 0$.

Equating real parts and imaginary parts would give us $a = 0$ and $b = 0$.

Therefore, $1$ and $2 i \pi$ are linearly independent, just as what is described in the definition.

--kc_kennylau (talk) 10:06, 24 December 2016 (EST)