Sheesh ... I completed bunches of math classes and this is more than Greek to me. I thought that space is curved and that is why parallel lines eventually meet. As for infinity, if we take an interval between 0 and 1, I seem to remember that we can continue halving that interval an infinite number of times ... with the limit being 0, but we never actually get to 0.
So, it seems that the answer to your question is that limit theory offers infinity within closed parameters. Chaos theory also offers infinite iterations with parameters, but we have to use our imaginations and imaginery numbers to get there. Mandelbrot sets is like an acid trip for computers ... chaos theory.
What sort of problem is physics having ... isn't physics a bit like applied math and engineering where you estimate the minimum, add a little and hope for the best? Okay, I'm not serious ... but it's not exactly like math theory.
Wait a minute ... don't most equations, whether the answer is infinity or not, have parameters? You know ... like :
-∞<x<∞, y>0, -1<z<1, t=10?
Clearly I don't understand the question.