Talk:Eplex

Transcendence
Schanuel's conjecture would imply the transcendence of Eplex:

Firstly, 10 is a nonzero algebraic number not equal to 1, so the Lindemann–Weierstrass theorem does imply the transcendence of ln(10).

Secondly, 1 and ln(10) are linearly independent over Q, so Q(1, ln(10), e, 10) has transcendence degree of at least 2 over Q. Therefore, ln(10) and e are algebraically independent over Q.

Thirdly, 1, ln(10), and ln(10)*e are linearly independent over Q, so Q(1, ln(10), ln(10)*e, e, 10, 10^e) has transcendence degree of at least 3 over Q. Therefore, ln(10), e, and 10^e are algebraically independent over Q, and the transcendence of Eplex follows. --84.61.186.220 19:51, September 29, 2014 (UTC)