TITLE: How can I succinctly but correctly say that a set is finite?
QUESTION [6 upvotes]: If I want to say that a set $A$ is numerable but infinite, I can do so like this: $$|A| = \aleph_0$$
What should I use instead to say that a set is finite? $|A|\in\mathbb{N}$? $|A|< \infty$? $|A|< \aleph_0$? Something else entirely?

REPLY [2 votes]: As a matter of style I would say, "$A$ is finite."  It is best to avoid having a bristling obstacle course of symbols for your reader to penetrate.  Which is easier to read here?
Every nonvoid subset of the positive integers has a least element.
$\forall \emptyset \subset S\subseteq {\Bbb N}$, $ \exists m\in S$ such that $m\le s$ $\forall s\in S.$
The choice is clear to me.  Use notation and symbols to simplify and clarify.