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Now go back and look at the original article: Does or does not the author abuse the use of the word "infinite" when he says the universe is infinite in size and mass?

What he said was:

space is infinite (or at least sufficiently large) in size and almost uniformly filled with matter, as observations indicate.

I consider that statement to be plainly stated and unavoidably correct, in light of very recent discoveries. It is possible that space does eventually curve back upon itself--see how Tegmark leaves that wiggle room--but we can tell that it is at least gigantically large compared to our horizon, or Hubble volume.

Perhaps we can discuss the use of the word "universe"; Tegmark refers to the space in which we live as the "Level-I Multiverse", reserving "universe" to refer to our Hubble volume, which certainly is finite, and which contains everything with which we can in principle travel to or interact with.

Star Trek:TNG had a great episode related to this subject, but instead what existed were quantum realities. Near the end of the episode, all the Enterprises started to appear. When "our" Enterprise tried to set everything straight, an alternate Riker in command of one of the ships said "We WONT go back! The Borg are everywhere!"

Kind of a chilling way to think of the alternate realities of Earth, perhaps one where Stalin ruled the planet?

Buggman: Now go back and look at the original article: Does or does not the author abuse the use of the word "infinite" when he says the universe is infinite in size and mass?

Actually, I think he's abusing the word infinite by assuming that it's all inclusive.

From his article, here is how he calculates the odds for someone's twin, not only existing in a parallel Hubble volume, but appearing in an infinite number of them.

One way to do the calculation is to ask how many protons could be packed into a Hubble volume at that temperature. The answer is 10^118 protons. Each of those particles may or may not, in fact, be present, which makes for 2 to the 10^118 possible arrangements of protons. A box containing that many Hubble volumes exhausts all the possibilities. If you round off the numbers, such a box is about 10 to the 10^118 meters across. Beyond that box, universes--including ours--must repeat. Roughly the same number could be derived by using thermodynamic or quantum-gravitational estimates of the total information content of the universe.

This shortcut may work for the early universe, but I don't see how it could work for a time when humans have already evolved. It looks like he's incorrectly assuming that a human can appear anywhere in the Hubble volume, but instead it must appear on the surface of a habitable planet. Not only that, but it must be on a planet where the quantum states of my parents appeared, and their parents, and so on all the way back to the primordial ooze. And then he goes on to make the following conclusion:

Your nearest doppelgänger is most likely to be much closer than these numbers suggest, given the processes of planet formation and biological evolution that tip the odds in your favor.

It seems to me that such required physical processes would greatly decrease the odds of my twin appearing in another Hubble volume.