I submitted the following question a few days ago, but it has not been posted as far as I can tell. Perhaps the submission did not go through, but it is also possible that it was not posted because someone thought that the question had already been asked. Just in case, I post it again. Please notice that my question is quite different from questions like "Is the universe infinite?" or "Does the universe have an end?".
So here it goes: Are there two points in the universe such that, if you take the straight line through these two points and lay out yard sticks along that line to measure the distance between those two points, no finite number of yard sticks is sufficient to do so. In other words, are there infinite distances in the universe?
Again, please notice that this is NOT the same question as "Is the universe infinite?" The universe could be infinite without there being an infinite distance between any two points. Many thanks for responding.
I believe that the answer to this question is "No". But it's a question for a physicist, really, not one for a philosopher nor even for a mathematician. One can certainly describe metrics on spaces that behave in the kind of way you suggest. But whether the universe is such a space is an empirical question.