Different kinds of infinity in physics?

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TL;DR Summary
Do different versions of infinity matter in physics?
I am reading several books on infinity as first developed by Georg Cantor.
Some physicists claim that the multiverse might be infinite. But they don’t seem to mention two of the kinds of infinity which might (exist?). It makes an infinite difference to make a bad pun. The integers define countable infinities but the real numbers are a larger infinity. I have read statements that if there are an infinite number of galaxies then there are an infinite number of myself in some infinite subset of this infinite multiverse. But that is not the case if this infinite number of galaxies is a countable infinity!
Don’t worry, I am not a mystic. I just find careless use of concepts unfortunate in scientific papers. Then again, many concepts are rather vague.

I just received the book “Beyond Spacetime” Ed. by Huggett, Matsubara and. Wuthrich.
Look very interesting.
I am also reading books and papers about gravitational waves — at last an experimental
field.
 

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