the infinite as the condition for the possibility of doing math

How mathematical operations require the infinite: they don't require an explicit affirmation of the infinite any more than reasoning requires an explicit affirmation of the principle of non-contradiction.  But they do require an openness to the applicability of the form of the operation to more numbers. And if numbers had a limit, X+1, where the operation would not work, then our knowledge about the form of the proposition would not be genuine knowledge.  We wouldn't even be able to know how to apply the operation to known numbers IF we denied that it could apply to others.  An openness to an unbounded applications is necessary in principle for us to be able to know what we do about numbers within the bounds that we have found them so far.