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transcendental number::noun | Spocien Dictionary
| Type | Words |
|---|---|
| Type of | irrational, irrational number |
| Has types | e, pi |
Examples of transcendental number
transcendental number
Unfortunately, not every transcendental number is a Liouville number.
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It is a normal and transcendental number which can be defined but cannot be completely computed.
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This has been proved to be a transcendental number.
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Using the explicit continued fraction expansion of e, one can show that e is an example of a transcendental number that is not Liouville.
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Whether a number is a closed-form number is related to whether a number is transcendental.
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No rational number is transcendental and all real transcendental numbers are irrational.
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Establishing that a given number is a Liouville number provides a useful tool for proving a given number is transcendental.
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The first number to be proven transcendental without having been specifically constructed for the purpose was e, by Charles Hermite in 1873.
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However, an algebraic function of several variables may yield an algebraic number when applied to transcendental numbers if these numbers are not algebraically independent.
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