id: 05955795
dt: j
an: 05955795
au: Nagata, Koji; Nakamura, Tadao
ti: Can the Peano axioms meet Zermelo-Fraenkel set theory with the axiom of
    choice?
so: Adv. Appl. Stat. Sci. 3, No. 1, 195-201 (2010).
py: 2010
pu: Mili Publications, Allahabad, Uttar Pradesh, India
la: EN
cc: 
ut: axiomatic set theory; number theory
ci: 
li: 
ab: 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.
rv: