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{{Short description|1960 mathematics textbook by Paul Halmos}}
{{Italic title}}
:''See also [[Naive set theory]] for the mathematical topic.''
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==Absence of the Axiom of Foundation==
As noted above, the book omits the [[Axiom of Foundation]] (also known as the Axiom of Regularity). Halmos repeatedly dances around the issue of whether or not a set can contain itself.
*p. 1: "a set may also be an element of some ''other'' set" (emphasis added)
*p. 3: "is <math>A</math> ∈ <math>A</math> ever true? It is certainly not true of any reasonable set that anyone has ever seen."
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==Errata==
*p. 4, line 18: “Cain and Abel” should be “Seth, Cain and Abel”.
*p. 30, line 10: "x onto y" should be "x into y".
*p. 73, line 19: "for each z in X" should be "for each a in X".
*p. 75, line 3: "if and only if x ∈ F(n)" should be "if and only if x = {b: S(n, b)}".
*p, 66, line 16: "Consider, for example, the set E of all those pairs (a,b) for which (1,1) <= (a,b); the set E has (1,1) for its least element.": the statement is not true, since (2,2) <= (1,1). In fact (2x2+1)x2^1 = 10 <= (2x1+1)x2^2 = 12.
==See also==
*[[List of important publications in mathematics]]
==Bibliography==
*[[Paul Halmos|Halmos, Paul]], ''Naive Set Theory''. Princeton, NJ: D. Van Nostrand Company, 1960. Reprinted by Springer-Verlag, New York, 1974. {{isbn|0-387-90092-6}} (Springer-Verlag edition). Reprinted by Martino Fine Books, 2011. {{isbn|978-1-61427-131-4}} (Paperback edition); [https://books.google.com/books?hl=en&lr=&id=bWu9DgAAQBAJ 2017 Dover reprint] {{isbn|9780486814872}}
==References==
{{reflist}}
[[Category:1960 non-fiction books]]
[[Category:Mathematics textbooks]]
[[Category:Springer Science+Business Media books]]
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