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First let me correct the terminology. I was sloppy when I said "the surface of a sphere". That's a weird thing to say because a sphere is a surface. The region "inside" the sphere is called a ball. For example, the set of all (x,y,z) that satisifes x2+y2+z2=r2 is called a sphere (or a 2-sphere to be even more precise), with radius r. The set of all (x,y,z) that satisifes x2+y2+z2<r2 is called an open ball of radius r. Replace the < with ≤ and the set is called a closed ball.Quantum-lept said:Yes, a circle or surface of a sphere has no edge or start/stop point.
But a sphere does have a boundary/edge.
A ball has a boundary. That boundary is a sphere. A sphere doesn't have a boundary.
When you say "sphere" here, you mean a "ball", and we are talking about spheres. 3-spheres to be exact. The homogeneous and isotropic solutions can be divided into three classes: positive curvature, zero curvature, and negative curvature. The zero curvature case is a lot like that infinite line with a time-dependent scale. The only difference is that a line is 1-dimensional and space is 3-dimensional. The positive curvature case is a lot like a sphere with a time-dependent radius. The only difference is that a sphere is 2-dimensional and space is 3-dimensional. So we should really be talking about a 3-sphere: w2+x2+y2+z2=r2Quantum-lept said:And we are speaking more of a sphere, which i think has an edge/boundary, moving though it may be.
You'd have to ask them, but I'm guessing that they're talking about the most distant objects we can see.Quantum-lept said:There are many references to the universe's edge by astrophysicists. What are they referring to?
Don't forget that now we're talking about a universe that's infinite at all times (the zero curvature case). There's no edge.Quantum-lept said:As for the universe expanding without changing size, that makes no sense. Though i admit that such a thing may be possible in this strange universe. Where are the galaxies on the edge of this universe going as they move away from all the others?