If the universe is finite in size, what is at the end of it?

[Jimmy Snyder]

The way I'm using the term, our universe doesn't necessarily refer to everything.

The OP asked about the universe.

 

[Pjpic]

opposition in terms

There must be other, more nuanced and technical, meanings to 'finite' and/or to 'unbounded' because to us 99.9 percenters finite actually means bounded.

 

[russ_watters]

That will be disconcerting news to racecar drivers...

 

[WannabeNewton]

Finite in this context does not mean bounded, it means compact. Bounded only makes sense in metric spaces and in general relativity we do not have a natural metric to impose on arbitrary space-time solutions. It is true that a subset of $\mathbb{R}^{n}$ is compact iff it is bounded and closed but space-time manifolds are not naturally embedded in a higher dimensional euclidean space. We must make use of topological notions when looking at global characteristics hence the term "finite" (which I agree with you is a horribly ambiguous and non-technical term) refers to compactness. I should note that for arbitrary topological spaces, compactness does not always bear resemblance to the intuitive notion of finiteness; what it does allow us to do is to turn local properties of a topological space into a global property so in this way it codifies a sense of the space being "finite" in a loose sense.