Mathematician here, hopefully I can clear up some confusion in this thread:

What I think this means to say is that it is finite butIt's finite, but its potential size is infinitely large.unbounded. We can find an easy example in terms of the natural (counting) numbers 1, 2, 3... and so on. Each number is finite, but they become arbitrarily large. However, under our current understanding, it is likely that a finite (i.e., closed - see the sphere analogy below) Universe would eventually stop expanding and collapse.

Sure it can, and we can construct simple examples depending on your precise definition of expansion. To use, say, two-dimensional area in the same way you would in a geometry class, consider a bar in the plane which extends infinitely far to the left and right, but is only one unit tall. It is easy to imagine such a bar expanding so that it remains infinite in extent to the left and right but is now two units tall. In both cases, the area is infinite, but in some sense the second object is "bigger" in the intuitive sense you're referring to.An infinite thing can't expand.

Not necessarily. Our current understanding of the Universe models it as an object called aIf it's finite, it has an edgemanifold. Roughly speaking, a manifold is an object that looks like normal Euclidean space as you did it in high school geometry, but only if you "zoom in" far enough. A simple example would be the surface of a sphere - if you stand at a point on the Earth's surface, the area around you looks like a plane. The surface of a sphere is finite in some sense (mathematically, we might say it hasfinite measureor iscompact, both of which have suitably rigorous definitions), but it has no boundary. It simply loops back around on itself. Similarly, our universe looks on a small scale like the usual three dimensions of space and one of time world that we're used to, but under extreme conditions or on large scales behaves differently. If our Universe is closed, it would be structured similarly to the sphere, except that the surface of a sphere is two-dimensional and our Universe to the best of our understanding is four-dimensional (although some speculative theories use many more).

False in almost any suitably rigorous sense. I direct you to Wikipedia's article on cardinality.Infinity is infinity! There's no bigger or smaller infinities!

The total energy can be infinite even if the density of that energy is not. Consider the plane filled with a uniform density of energy, so that the amount of energy contained in a region is proportional to the area of that region. Since we, and any other point in the universe, can only observe a finite volume at any finite time due to speed-of-light constraints, the total energy of the universe may well be infinite even if the energy we observe is always finite.There's just no evidence of an infinite amount of energy in the universe. Sure, there is a lot of it, but no matter how far it expands or how long it goes on it's still a finite number.

Matter cannot move faster than light under current physical understanding. But this expansion is not motion in the normal sense - roughly speaking, the way the Universe measures distances is, over time, measuring larger and larger ones even between objects that are not (with respect to their own space) moving. The effect is tiny enough to be unobservable at small scales (within, say, a galaxy), but in the voids between galaxies it dominates, and it is not limited by speed-of-light concerns because proper motion is not involved. In addition, objects that we see today emitted the light we see when they were considerably closer to us than they are now.Now how is that supposed to work? If we follow the Big Bang, this universe started condensed in one spot. So you're telling me that, in 13.7 billion years, it managed to expand ~6.78 x the speed of light?

Something seems off about this math.

For instance, suppose we all lived on a straight line where distances double every year (and for the sake of keeping calculus out of things, let's assume that doubling happens instantaneously at 12:01 January 1), and where the speed of light is two units/year. An object that emitted light one year ago on December 31, 2000, when the distance between us and the object was 1 unit, would be seen by us on December 31, 2001 as it was on December 30, 2000 - but as we see it, that object is now two units away from us even if it didn't "move" with respect to its own space. Such an object would cease to be visible eventually. This analogy isverysimplified and ignores the fact that there is no absolute notion of "distance in space" in the Universe, but it serves to illustrate the point.