Euler's Number is Transcendental/Proof 2

Theorem

Euler's Number $e$ is transcendental.


Proof


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$\blacksquare$


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

  • 2004: Ian Stewart: Galois Theory (3rd ed.)
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