Re:Conterintuitive facts in mathematics, CS, and physics
by adenadel on Tuesday October 05, 2021 @09:51PM
(#28768272)
In fact, almost all numbers are transcendental (algebraic numbers have measure zero).
Re:Conterintuitive facts in mathematics, CS, and physics
by bloak on Wednesday October 06, 2021 @03:37AM
(#28770261)
I agree. Probably most people who know what "transcendental" means would guess that the number described is transcendental.
However, only a small proportion of people who know what "transcendental" means are capable of proving that any number is transcendental.
> Let alpha = 0.110001000000000000000001000..., where the 1's occur in the n! place, for each n. Then alpha is transcendental. (Calculus, 4th edition by Michael Spivak)
Nearly all infinite sums involving factorial are transcendental.