# Can monotone classes be finite?

I am new to measure theory and real analysis and am trying to double check my understanding of monotone classes.

My question:

Can monotone classes be finite? (It is not clear to me whether the idea of increasing or decreasing sets refers to STRICTLY increasing or decreasing sets.)

A related question:

Is any subset of a monotone class itself a monotone class? (The reason I ask is that I do now know the answer to the previous question.)

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An example of a finite monotone class of a set $X$ is $\{\varnothing\}$.
An example of a subset of a monotone class that is not itself a monotone class is the subset $$\{\text{finite subsets of }\mathbb{N}\}\subset\mathcal{P}(\mathbb{N}).$$ The power set of $\mathbb{N}$, $\mathcal{P}(\mathbb{N})$, is certainly a monotone class, but the increasing sequence of sets $$\varnothing\subset\{1\}\subset\{1,2\}\subset\cdots$$ each of which lies in the set $\{\text{finite subsets of }\mathbb{N}\}$, has a union of $\mathbb{N}$, which is not in that set.