Actual Infinity in Reality?

[polymath257]

OK, so to be clear. There is no 'outside' of spacetime. There is an outside of any particular spatial cross section (any other spatial cross section). But the collection of *all* such cross sections is 'spacetime'.

And again, the best answer to what the universe is expanding into, even for finite space, is 'the future'.

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Hmmm...a finite space does NOT imply an outside. That may be one of the issues here.

So, suppose that space is curved. In practice, what that means is that whatever direction you set off, if you keep going you will eventually come back around to your starting point (no actual travel--stay on one spatial cross section). So, you decide to take off in the 'up' direction and travel for a few billion light years, you will come back around to the start from the 'south' direction. Same with East vs West, and any direction and its opposite.

The reason I say not to actually travel is the time aspect of such: motion requires time and the time it would take to go 'around' is enough that the size changes during the trip.

So, just take a specific spatial cross section and go off in one direction, staying on that cross section. Eventually, with a finite space, you will come back around.

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Also, don't confuse the 'totality of all existence' with the 'totality of space at this time'.

Ok, so what you're saying (in the case of a finite universe) is that 'the totality of space at a certain time' is finite in the sense that eventually if you "movelessly" go across its full length (or whatever) in one direction, you eventually reach the point where you first began "movelessly" going (so basically a loop). Sort of like the surface of a ball, but we need to think in a higher dimension instead. IOW, finite does not always imply "edge". Did I get you right?

Yes. Finite in volume only. No edge