Hmm, that could potentially cause confusion later. There are 'countable' and 'uncountable' forms of infinity / infinite sets.
A countably infinite set could be 'counted' (i.e., you could sit around labeling elements using the 'natural' or 'counting' numbers) in the sense that we might count candy. The issue for a human being is that you'd run out of time but not elements to count, at least, proceeding in the sense one might count the candy - a piece at a time. Of course, you can, instead, simply provide a 'bijection' (between the natural numbers and the set you wish to prove is countably infinite), and in a sense, you are done.
The subject of infinity and infinite sets can be kind of subtle, and for years the best mathematicians made many mistakes and had many difficulties handling these concepts in ways that didn't cause potentially serious problems (absurdities, paradoxes, etc.). I think that with the development of things like Zermelo-Fraenkel set theory, Gödel's incompleteness theorems, etc., things became a lot clearer. It's a lot easier, with all of the groundwork laid by people who worked on these, to get a good sense of what is possible and what isn't - what gets you into trouble and what doesn't. But, boy, did it twist the minds of the people trying to work it out at the time. In part, this is because it was less clear, without development in these areas, what math even is and what its limits are ... what its relationship to the structure of the universe, say, even is (something along those lines, in my opinion / experience).