Wouldn't even reincarnation have to reach an ending, eventually?

Surely even science doesn't allow for something, let's say reincarnation for argument sake even, to be logically or scientifically possible to be infinite and instead finite? Surely isn't even the galaxy or the world limited in size itself? I don't get it lol.
It is finite
It is infinite
For argument sake, more research and understanding is needed
I heard the universe is constantly expanding, so maybe reincarnation, could have infinite realms, for the sake of the question ⁉️
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Wouldn't even reincarnation have to reach an ending, eventually?
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