Irrationnalité de $\mathrm{e}$

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Théorème

La constante
$\mathrm{e}=1+\frac{1}{1}+\frac{1}{1\times 2}+\frac{1}{1\times 2 \times 3}+\ldots =\sum_{n=0}^{+\infty}\frac{1}{n!}$ $=\lim_{n\rightarrow +\infty}\left(1+\frac{1}{n}\right)^{n}$ $\mathrm{e} \approx 2.718281828459...$

est irrationnelle.
Le premier à le montrer est L. Euler en 1737.

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