It has been suggested that space and beyond is infinite, but admittedly the same hypothesis was made by virtue of the fact that it is physically impossible to prove otherwise.

How do we know that there is no border at the end of "infinite" space?

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    $\begingroup$ I'm presuming "it has been suggested" means that science has suggested it. The correct way to read phrases like that are terribly exacting, and might be better phrased "We have not falsified the theory that space is well modeled as an infinite space in all directions." The steps it takes to go from there to "space and beyond is infinite" are simplifications, and they are exactly the kind of simplifications that are causing you grief. $\endgroup$ – Cort Ammon Apr 6 '16 at 3:14
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    $\begingroup$ @PatJ: Or on Physics - the subject matter tends to overlap. But the OP would do better to read a recent popular book on cosmology - there are probably a number available at your public library - since a good answer is going to be longer than most people would care to type. $\endgroup$ – jamesqf Apr 6 '16 at 4:38
  • $\begingroup$ If you are interested in the storytelling aspect rather than strict theory, try worldbuilding.stackexchange.com/questions/30957/… $\endgroup$ – Kys Apr 6 '16 at 16:26
  • $\begingroup$ Funny, I always thought that part of the definition of infinity is that it has no end. So how can you suggest that infinity can have a border? $\endgroup$ – WhatRoughBeast Apr 7 '16 at 0:59
  • $\begingroup$ What is beyond the known observable universe? No-one knows. We do not know what lies beyond that which we can see. $\endgroup$ – MichaelK Apr 7 '16 at 6:23

We do not know what lies beyond the limits of our instruments, by definition.

For all we know, there could be a big sign saying "This area under construction."

However, that doesn't seem very probable.

The most probable answer is "more of the same". After all, there is no reason the bit of the universe we can see should be different from other places.

If you keep adding "more of the same" to the universe, you get the infinite universe you have seen described.

It is just a theory, but it seems like a pretty probable one.

It is also easier to do calculations on. Having a border introduces all kinds of problems like galaxies near the border only getting gravitational forces from one side only. With an infinite universe these forces come from all directions and cancel each other.

It is still just a theory, but it is one that is (relatively) easy to work with.