Cardinality of Infinite Sigma-Algebra is at Least Cardinality of Continuum/Corollary

Corollary to Cardinality of Infinite Sigma-Algebra is at Least Cardinality of Continuum
Let $\MM$ be an infinite $\sigma$-algebra on a set $X$.

Then $\MM$ is uncountable.

Proof
From Cardinality of Infinite Sigma-Algebra is at Least Cardinality of Continuum, $\MM$ has at least the cardinality of the set of real numbers $\R$.

The result follows from Real Numbers are Uncountable.