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Hello,

Hello, 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.

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.

I understand points as entities with zero extension. (Is this correct?) Yet

I understand points as entities with zero extension. (Is this correct?) Yet infinitely many points are said to compose space. It seems like even infinitely many zeros could never add up to a finite non-zero value. So, what's up with points? If they don't have any extension, what are they? As a follow up, does it make sense to think about points in space in a different way from how we think about points in time?

Yes, a point has length, depth, and height zero. So do two points, three points, and even as many points as there are natural numbers. But if you have as many points as there are real numbers (of which there are more than there are natural numbers), then that set of points may have some positive length, depth, or height, though it may not. (In that case, they will not have zero length, depth, and height but may have no assignable length, depth, or height.) The branch of mathematics in which such things are studied is called "measure theory".

Exactly what a point is is another question. In mathematics, points may be regarded in a wide variety of ways, as is convenient. Are there any points in space itself? That's a disputed question, and an empirical one, not one on which philosophers can pronounce.

Yes, a point has length, depth, and height zero. So do two points, three points, and even as many points as there are natural numbers. But if you have as many points as there are real numbers (of which there are more than there are natural numbers), then that set of points may have some positive length, depth, or height, though it may not. (In that case, they will not have zero length, depth, and height but may have no assignable length, depth, or height.) The branch of mathematics in which such things are studied is called "measure theory". Exactly what a point is is another question. In mathematics, points may be regarded in a wide variety of ways, as is convenient. Are there any points in space itself? That's a disputed question, and an empirical one, not one on which philosophers can pronounce.

Where does the universe end?

Where does the universe end?

The answer to question 50 is also an answer to this question, I think: The universe doesn't have an end.