I agree. The practical intuitive way to think about “infinity” I use is to simply use a variable N that can be arbitrarily large. And then reason about f(N). It

I agree. The practical intuitive way to think about “infinity” I use is to simply use a variable N that can be arbitrarily large. And then reason about f(N). It stops you from asking nonsenses like “what is infinity divided by infinity?” since you have to explicitly use N when asking the question. As in “what is f(N)/g(M) for arbitrarily large numbers N and M?”. Which gives you a straightforward way to answer the question.