Question

How to prove that there’s always at least one rational number between two real numbers?

Answer 1

See explanation...

Explanation:

Given two real numbers `a < b`, choose an integer `N > 1/(b-a)`

Then `b-a > 1/N`

If `b` is an integer multiple of `1/N` then `b-1/N` is a rational number in `(a, b)`

Otherwise `floor(bN)/N` is a rational number in `(a, b)`