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Question

How do you prove a number, like e or pi, to be transcendental?
Asked by: Nathan Douglass

Answer

There is no general theorem that identifies transcendental numbers to my knowledge. However, there are theorems that do so for special cases. Of these theorems, Gelfond's theorem is probably the most useful. It states: If a number 'r' is not the root of any polynomial equation with integer coefficients of any degree, then 'r' is transcendental.

Cantor proved the existence of transcendental numbers. Hermite (1873) proved that the number 'e' is transcendental. Lindemann (1882)proved that 'pi' is transcendental.
Answered by: Vince Calder, Ph.D., Physical Chemist, retired


Answer

You can find a fantastic explanation of transcendental numbers, and their history at the following website: http://mathworld.wolfram.com/TranscendentalNumber.html
Answered by: Eric Baicy, B.S., Seattle






Science Quote

'Physics is mathematical not because we know so much about the physical world, but because we know so little; it is only its mathematical properties that we can discover.'

Bertrand Russell
(1872-1970)





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