Difference between revisions of "E"
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Revision as of 18:58, 24 May 2016
The number $e$ can be defined in the following way: let $f$ be the unique solution of the initial value problem $$y'=y;y(0)=1,$$ then $e=f(1)$.
Properties
Theorem: The folllowing formula holds: $$e=\displaystyle\lim_{k \rightarrow \infty} \left( 1 + \dfrac{1}{k} \right)^k,$$ where $e$ denotes Euler's constant.
Proof: █
Theorem: The real number $e$ is irrational.
Proof: proof goes here █
