The Infinite Replication Paradox

In chapter four of his book, The Infinite Book, John D. Barrows opens with the following paragraph:

Imagine living in a universe where nothing is original. Everything is a fake.
No ideas are ever new. There is no novelty, no originality. Nothing is ever
done for the first time and nothing will ever be done for the last time. Nothing
is unique. Everyone possesses not just one double but an unlimited number
of them. (page 155)

His statement is based on the probability that in a universe of infinite size, anything that has a nonzero opportunity to happen must occur infinitely often. Recent cosmological research involving inflation, QM, and M theory support the following tentative conclusions:

1.The universe is infinite and/or is part of an infinite multiverse.
2.There are only a finite number of variations for a universe and its contents to possess without being duplicated.

The first premise is based on astronomical observations of the shape of the universe and also on the eternal and chaotic inflation models of the early universe. The second premise is derived from the limited number of configurations of a universe allowed by M Theory. About 10 to the power of 500 (10^500).

The correctness of these two premises has profound philosophical implications. Within the context of infinity, a duplicate of our own universe will occur an infinite number of times. This implies each one of us have an infinite number or exact duplicates performing all of the activities we have or have not done. There would be an infinite number of duplicates reading this message and an infinite number doing something else. Our duplicates would be born an infinite number of times and die an infinite number of deaths. There would be an infinite number of world wars, an infinite number of Hitlers and Stalins. Suffering and pain would occur an infinite number of times. Incidentally, St. Augustine rejected eternal re-occurrence because Christ would have had to been crucified an infinite number of times!

I have several questions if the above two premises are true. If my duplicates are indiscernible are they all the same person with the same identity? When we die do we get reborn as one of our duplicates? Do we ever die or do we become one of the remaining surviving duplicates? Is there any natural way rather than a supernatural being that could prevent the duplication of universes and people?

Well why would one assume that anything that has a nonzero probability must occur infinitely often in a universe of infinite size?

(p>0)*∞ = ∞

Um how does that help? You're going to apply this equation somehow? What are the units for these values in your equation?

Suppose a 52 deck of playing cards has been shuffling for eternity. After 80658175170943878571660636856403766975289505440883277824000000000000 shuffles the order of the deck would start repeating itself. If this shuffling has been going on for an infinite number of times, all possible arrangement would have occurred an infinite number of times for eternity. There would be an infinite probability this wold happen.

If something is infinite in space and time, must it include everything that is possible too? And given the "arrow of time" there is no reason to think history should repeat itself -- it might be more true to the meaning of "infinite" to think of things as infinitely variable!