Editing Naive Set Theory (book) (section)

==Notes==

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: <small>[a]</small> - In fact given the rest of the axioms, neither of the original Zermelo axiom of infinity, nor Halmos' axiom of infinity, can be proven from the other,<ref>{{cite journal |last1=Drabbe |first1=Jean |title=Les axiomes de l'infini dans la théorie des ensembles sans axiome de substitution |journal=Comptes Rendus de l'Académie des Sciences de Paris |date=20 January 1969 |volume=268 |pages=137–138 |url=https://gallica.bnf.fr/ark:/12148/bpt6k480296q/f140.item |access-date=8 September 2024}}</ref> even if one adds in the axiom of foundation. That is, one cannot construct the infinite set Halmos' axiom asserts exists, from the infinite set Zermelo's original axioms assert exists, and vice versa. The axiom schema of Replacement, on the other hand, ''does'' allow the construction of either of these infinite sets from the other.
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