# Able to define definable

Calculus Level 4

A definable number is a real number $$a$$ such that, given a formula in the language of set theory $$\varphi$$, $$\varphi(a)$$ is true. Thus, definable numbers include constants like $$0, 1, e, \pi$$ and so on.

What is the Lebesgue measure of the set of all definable numbers in the interval $$(0,1)$$?

×