algebra generated by a countable set is countable How to prove that algebra generated by a countable set is countable. Hint enough. I know that algebra generated by any set $A$ is of the form $\cup_{i=1}^{m}\cap_{j=1}^{n_i} A_{ij}$ where $A_{ij}$ or $A_{ij}^c$ is in $A$.

HINT: Every set in the algebra has a "generating sequence" which is a finite sequence including the sets and indices over which we union and intersect. Note that if $A$ is a countable set then set of finite sequences from $A$ is countable.
