The Continuum Hypothesis

Tries to answer The Continuum Problem
The size of is the smallest possible!
In other words:

Theorem (Gödel)

We can’t refute the Continuum Hypothesis.
More precisely, if Zermelo-Fraenkel Set Theory is consistent
then

Proof

Follows from the Technique of Inner Models.

Theorem (Cohen)

We can’t prove the Continuum Hypothesis.
More precisely, if Zermelo-Fraenkel Set Theory is consistent
then