THEOREM OF THE DAY: The Lindemann-Weierstrass Theorem

Theorem

If $α_1, . . . , α_n, n ≥ 1$, are algebraic numbers which are linearly independent over $Q$, then $e^{α_1}, . . . , e^{α_n}$ are algebraically independent; that is, any rational polynomial $P(z_1, . . . ,z_n)$, having algebraic coefficients, for which $P(e^{α_1}, . . . , e^{α_n}) = 0$, must be identically zero.

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