Euler's Number is Transcendental/Proof 2

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Theorem

Euler's Number $e$ is transcendental.


Proof


$\blacksquare$


Historical Note

The transcendental nature of Euler's number $e$ was conjectured by Joseph Liouville in $1844$, after he had proved that it was not the root of a quadratic equation with integer coefficients.


The proof that $e$ is transcendental was first achieved by Charles Hermite in $1873$.


Sources