Lindemann–Weierstrass theorem

In transcendental number theory, the Lindemann–Weierstrass theorem is a result that is very useful in establishing the transcendence of numbers. It states the following: In other words, the extension field Q ( e α 1 , … , e α n ) {\displaystyle \mathbb {Q} (e^{\alpha _{1}},\dots ,e^{\alpha _{n}})} has transcendence degree n over Q {\displaystyle \mathbb {Q} } .