At the end of this process, we never ended up in a position where it was necessary to claim the existence of infinity or
You generally “must” assume the “existence” of numbers behind finite positive integers in order that solve certain kinds of problem. By that’s a hypothetical “must”, not a categorical one. You can sacrifice the ability to solve those problems as an alternative.
that numbers have an objective non-mind-dependent, non-physical existence.
None of the above requires existence in a serious ontological sense.
You generally “must” assume the “existence” of numbers behind finite positive integers in order that solve certain kinds of problem. By that’s a hypothetical “must”, not a categorical one. You can sacrifice the ability to solve those problems as an alternative.
None of the above requires existence in a serious ontological sense.