Transcendental number

Table of contents
- Hermite theorem on the transcendence of e Transcendental number
- Liouville number Transcendental number

Hermite theorem on the transcendence of e ( $e \in / \overline{Q}$ )

The Hermite theorem states that the base

e

of the natural logarithm is a transcendental number.

Liouville number

A Liouville number admits rational approximations of every fixed polynomial order; Liouville's approximation theorem makes every such irrational number transcendental.

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Transcendental number by

Ciro Santilli  40 Updated 2025-07-16

Sometimes mathematicians go a little overboard with their naming.

Bibliography:

www.quantamagazine.org/recounting-the-history-of-maths-transcendental-numbers-20230627/

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