This NPR article got me thinking: why wouldn't it be true that parallel universes must exist. Of course the term universe is being used rather loosely, if the universe IS infinite, there couldn't be a parallel universe, only a parallel containment unit within the universe (such as a parallel galaxy).
After a bit of thinking I realized that the hypothesis is false if you accept the idea from my previous post that the universe is not only infinitely big, but infinitely precise. The infinite precision would allow for an infinitely sized universe with no requirement that there ever be a 'parallel' containment unit.
There is probably some proof of this idea in set theory somewhere, but as a philosopher, I have immunity from having to come up with proofs. Maybe if there's a mathematician out there they can supply that. A good place to start might be this wikipedia article
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