Difference between revisions of "E"
From specialfunctionswiki
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$$y'=y;y(0)=1,$$ | $$y'=y;y(0)=1,$$ | ||
then $e=f(1)$. | then $e=f(1)$. | ||
| + | |||
| + | =Properties= | ||
| + | <div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> | ||
| + | <strong>Theorem:</strong> The real number $e$ is [[irrational]]. | ||
| + | <div class="mw-collapsible-content"> | ||
| + | <strong>Proof:</strong> proof goes here █ | ||
| + | </div> | ||
| + | </div> | ||
=References= | =References= | ||
[http://eulerarchive.maa.org/hedi/HEDI-2006-02.pdf Who proved $e$ is irrational?] | [http://eulerarchive.maa.org/hedi/HEDI-2006-02.pdf Who proved $e$ is irrational?] | ||
Revision as of 02:29, 3 October 2014
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 real number $e$ is irrational.
Proof: proof goes here █
