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

  • Thread starter Kutt
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  • #51
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The way I'm using the term, our universe doesn't necessarily refer to everything.
The OP asked about the universe.
 
  • #52
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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.
 
  • #53
russ_watters
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That will be disconcerting news to racecar drivers...
 
  • #54
WannabeNewton
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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.
 
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