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\iteman{io-port 05955795}
\itemau{Nagata, Koji; Nakamura, Tadao}
\itemti{Can the Peano axioms meet Zermelo-Fraenkel set theory with the axiom of choice?}
\itemso{Adv. Appl. Stat. Sci. 3, No. 1, 195-201 (2010).}
\itemab
Summary: We show that the Peano axioms do not meet the ZFC axioms. We discuss that the set of natural numbers, i.e., $\{1,2,\dots\}$, does not meet the ZFC axioms. We know that such a set of natural numbers is a representation of the Peano axioms. Hence the Peano axioms do not meet the ZFC axioms. Our discussion relies on the validity of addition, subtraction, multiplication and division.
\itemrv{~}
\itemcc{}
\itemut{axiomatic set theory; number theory}
\itemli{}
\end