According to the axiom of replacement, the von Neumann hierarchy of sets just keeps going.
You mean injective functions, for finite M,N? True, but does it relate to the von Neumann hierarchy just keeping going?
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I mean just a dumb joke about permutations vs. combinations (which may be the same joke you were making for all I know, but I couldn't quite figure it out.)
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Oh! I did not get it at first. I wasn't really making a joke, just noting that the axiom of replacement is what prevents the ordinals from stopping at some point that can be described from below.
End of conversation
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