I'd like to know what is thought of when saying the universe is infinite.

I've read about what is meant when astronomers are speaking of a "flat" universe and I have read that its size is most likely infinite. Yet Google couldn't forward me to a site where it's actually explained what that should mean.

These are some sites I looked but which did not explain it:

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    $\begingroup$ possible duplicate of Is the universe finite or infinite? $\endgroup$ – John Rennie Feb 6 '15 at 8:29
  • $\begingroup$ Also see this search for lots of other related questions. $\endgroup$ – John Rennie Feb 6 '15 at 8:30
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    $\begingroup$ That link is the first of the 5 that I linked in my post. It's not explained there - I'm not asking whether or not the universe is infinite but what is meant when saying that it is infinite. $\endgroup$ – mYnDstrEAm Feb 6 '15 at 8:33
  • $\begingroup$ infinite means that is not finite as a set; i.e. there is no natural number $n$ (seen as a set of $n$ objects) with which each of its objects can be put in one to one correspondence. The existence of such a set however cannot be proved, it is an axiom $\endgroup$ – yuggib Feb 6 '15 at 8:45
  • $\begingroup$ @yuggib I don't think that is usually meant when saying the universe is finite or infinite. It rather refers to it being bounded or unbounded, or compact or not if you want. $\endgroup$ – doetoe Feb 6 '15 at 8:53

The observable universe is not infinite because the light near to the big bang took a finite time to get here at a finite speed.

Consider a young galaxy seen in the Hubble deep field.

young galaxy

Where that galaxy is today, an observer living there can also see our galaxy as it was very young (with their own Hubble telescope).

Looking in the opposite direction, that observer can see other galaxies that we have never seen and never will do. Those are not in the observable universe.

Now consider another observer in one of those galaxies, and suppose he/she/other did the same.

That series of observers could continue much, much, much further. And maybe does too.

This could be described as a long, long, long series of overlapping light cones, but please check on this !

But we only have indirect evidence of the length of this series. Somebody saying that the universe is infinite, considers that this series of observers is not just very, very, very long, but infinite.

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