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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. (Cal
by campital 5y ago
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.
- bloak 5y agoI 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.
- adenadel 5y agoIn fact, almost all numbers are transcendental (algebraic numbers have measure zero).