Generated Sigma-Algebra Preserves Finiteness

Theorem
Let $X$ be a set, and let $A_1, \ldots, A_n \subseteq X$ be subsets of $X$.

Then $\sigma \left({\left\{{A_1, \ldots, A_n}\right\}}\right)$ is finite, where $\sigma$ denotes generated $\sigma$-algebra.