It really depends. For example, if you walk 1m, then 0.5m, then 0.25m and continue infinitely, then "after infinity" you will have walked exactly 2m. This is the classic 'Achilles and turtle' example and works fine if the value converges. It's just mathematics.

There is only a problem if the value diverges. Imagine the step example, but on even steps, you raise a blue flag, and on odd steps you raise a red flag. Now the question what flag is raised "after infinity" is impossible to answer. It clearly should be either red or blue, but it also can't really be either, because that would mean infinity is either even or odd, which makes no sense.