yes, the big bang theory does suggest that the universe is expanding. I'm not sure, but I think it's that red shift thing that proves that. Anyway, i agree, something that expanding cannot be infinite,
but,
That theory is describing our observable universe, and not the universe as a whole. The dictionary's definition is something like, everything in existance. We can't see everything, thus we cannot know.
there are newer theories and studies, that describe the whole universe as multiple expanding universes like ours. Simmons touched on it, with the bubble analogy. From memory, the universe that we see, is one of many, on many different membranes. You can picture it as a ballon, with many dots on it. Our observable universe is one of the many dots, and the balloon, is one of many membranes. As you blow up the balloon, the dots expand, and move further away from each other without ever touching.
i throw the word membrane around like I'm an expert. Really though, I havn't been able to grasp that idea yet. Same with extra dimensions. They both hurt my head.