How to construct an algebra / field that is infinitely countable? It is well-known that a $\sigma$-algebra / $\sigma$-field can only be finite or uncountable infinite, but how to construct an example of algebra / field that is infinitely countable? This is actually a question from Billingsley's Probability and Measure problem 2.12.

An example is the collection of finite unions of intervals in $\Bbb{R}$ with end points in $\Bbb{Q}\cup \{\infty, -\infty\}$.
