### Abstract

This work contains a proof that Euler's number e is transcendental. The proof follows the standard approach of assuming that e is algebraic and then using a specific integer polynomial to derive two inconsistent bounds, leading to a contradiction.

This kind of approach can be found in many different sources; this formalisation mostly follows a PlanetMath article by Roger Lipsett.

### License

BSD License

### Topics

- Mathematics/Analysis
- Mathematics/Number theory

### Session E_Transcendental

- E_Transcendental

### Used by

- The Irrationality of ζ(3)
- The Transcendence of π

## Cite

×

E_Transcendental-AFP

    @article{E_Transcendental-AFP,
      author  = {Manuel Eberl},
      title   = {The Transcendence of e},
      journal = {Archive of Formal Proofs},
      month   = {January},
      year    = {2017},
      note    = {\url{https://isa-afp.org/entries/E_Transcendental.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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