VIII. Final Thoughts
The fact that we have shown the existence of f : ℕ → [r1, r2] implies that Cantor’s continuum hypothesis is true for closed intervals of real numbers. Interestingly, it’s not that there are no infinite sets with cardinality between ℵ0 and ℵ1, rather ℕ and [r1, r2] turn out to be the same size.