I don’t think it really is a particularly math-specific concept. I mean, it is mathematical in the same way that “how many fingers am I holding up?” is mathemat

I don’t think it really is a particularly math-specific concept. I mean, it is mathematical in the same way that “how many fingers am I holding up?” is mathematical, but it isn’t specific to any particular axiomatization of something, and is instead expressed in terms of general intuitive notions. If I have a box, I might ask, “is there some number n such that there are fewer than n protons in this box?”. Well, really, the question would be phrased “are there finitely many protons in the box”, but I’m avoiding the word “finite” because you use the word “infinite” differently. The question of “are there ‘un-split-able ones’ ?” goes way back, and is a question about the world, not about math considered abstractly. Aiui, it was considered philosophically. A question as to whether there is a limit to how much things can be split into smaller parts. The question of “Does this thing have a limit of ‘how much’/‘how many’ ?“ is not a question which concerns only mathematicians, but which concerns anyone who seeks to understand the world.