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How is 27 counterintuitive?

> 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.




In fact, almost all numbers are transcendental (algebraic numbers have measure zero).


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.




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