In set theory "naive" and "axiomatic" are contrasting words. The present treatment might best be described as axiomatic set theory from the naive point of view. It is axiomatic in that some axioms for set theory are stated and used as the basis of all subsequent proofs. It is naive in that the language and notation are those of ordinary informal (but for- malizable) mathematics.
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Jack-Rustier - (no access) - (Undergraduate Texts in Mathematics) Paul R. Halmos (auth.)-Naive Set Theory-Springer-Verlag New York (1974).pdf, p6
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