Transcendental number
Builds on Algebraic number
Definition
A complex number is transcendental if it is not an algebraic number. That is, it is not a root of any nonzero polynomial with rational coefficients.
Remarks
The numbers and are transcendental, by the Lindemann–Weierstrass theorem. Each Liouville number is transcendental, by Liouville's theorem. The algebraic numbers are countable, so almost all real numbers are transcendental. Joseph Liouville first proved that transcendental numbers exist, in 1844.
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- Algebraic number definition
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Further reading
- Web https://en.wikipedia.org/wiki/Transcendental_number, lead section
About this page
| Tag | 079EGSD32Y |
|---|---|
| URI | m2://079EGSD32Y |
| Kind | definition |
| Writing | W1 stated |
| MSC | 11J81 |
| Defines | Transcendental number |
| Uses | Algebraic number |
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What this page needs for W2
- edge not_instance_of in: one non-example that fails one clause (0 of 1)
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