Lebesgue measure of transcendental numbers in $[0,1]$.

Question

What is the Lebesgue measure of the transcendental numbers in the $[0,1]$ interval? I was not able to find any information on this. (Does this question even make sense given what we currently know about transcendental numbers?)

Thanks.

Answer 1

The algebraic numbers are countable (a basic exercise in every undergraduate real analysis text). Countable sets have measure zero, so the complement has full measure ($=1$).

Answer 2

HINT: The algebraic numbers are countable.