# Transcendence

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Boris Alexeev
Fine Hall 314

We all know that e and π are transcendental. How about numbers like $e+π$, $e^π$, or $sqrt(2)^[sqrt(2)]$ If $2n$, $3n$, and $5n$ are all integers, must $n$ be an integer as well? What if only $2n$ and $3n$ are integers? In this talk, I will talk about these and related questions. In particular, I hope to prove the well-known fact above: $e$ and $π$ are transcendental. I will also mention the applications of transcendence theory to other subjects, like logic and integration.