Proving the universe is infinite I think he idea of infinity/eternity is simply impossible, it cannot exist. It can be demonstrated, as far as we know, and as far as computers can calculate, with mathematics, but that doesn't say anything about the possibility of infinity in the real world.
"The only constant is change."
Science makes a pretty good case that the universe we inhabit is finite, so one could speculate that there has to be something outside of our universe, something different. But it is impossible, so far, for science to see what that might be, or the extent of it, so currently the topic is moot.