[campital]

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.

[adenadel]

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

[bloak]

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.