NOTE: Taken from another thread on a similar subject:
http://www.physicsforums.com/showthread.php?t=125698
Quote by loseyourname
Well, the main questions were two:
1) Is there an infinite amount of matter in the universe?
2) Did Tegmark actually make that claim?

"An infinite amount of space with matter uniformly distributed throughout", is not a claim of infinite matter – at least it shouldn't be.
If matter is assumed to be inside of a greater space that is infinite – then matter is necessarily less than infinite.
I would hope his point, is simply about the uniformity of distribution at the infinitesimal. This is quite possible.
Otherwise, it's just a shortsighted rehash of a relative ad infinitum.
One way of looking at an open and closed model is this:
A closed model has an edge – because matter is outside of space.
An open model has no edge – because space is outside of matter.
Another way of looking at them is this:
A closed model – has both matter and space as finite.
An open model – ha both matter and space as infinite.
A closed model – has a big bang and crunch.
An open model – has no big bang and crunch.
Finite – has a beginning and end.
Infinite – has no beginning or end.
Finite – means the universe began, is, and will stop "actually" happening.
Infinte – means the universe is always in the state of potential of "will happen".
Either way, however – we can't tell unless we know what is outside the universe. Any description of the universe as "all" – begs the same question. What is outside of it? Space and matter are only capable of being a relative ad infinitum. Without an absolute there is no answer.
Is the Absolute inside or outside the universe? It can't be both.