# Is the book "Naive Set Theory" authored by P. R. Halmos still up-to-date?

My question is whether Halmos' book "Naive Set Theory" is still up-to-date concerning contemporary mathematics; that is, is it outdated or not?

I really love the book so far, and while it's clear the notation is outdated, so far nothing contradicts what we had in the lectures. My assistant in calculus warned me about the book not being the newest though, so I'm a little confused right now.

Can I safely continue reading it without learning anything wrong or should I look for another book? If the latter is the case, can anyone of you give me a suggestion which book would be better suited?

Sincerely, SDV

• I haven't read it, or thoroughly reviewed it (with the exception of several questions about the Zorn-choice equivalence, as I remarked below Ittay's answer); but I can say that I looked over Enderton's book and it looks really nice. If you want to learn to read Hebrew, Azriel Levy has excellent notes in Hebrew about naive set theory (unrelated to his book which is a bit more advanced). In any case, the fundamentals of set theory haven't change since Halmos wrote the book, so you don't need to worry about learning wrong things. Oct 19, 2014 at 15:23
• The book becomes aa bit difficult for self study at a point ( because explanations are too concise). . I've found Enderton 's book more reader friendly. ( Also, for a complete beginning, you may have a look at Seymour Lipschutz' Theory And Problems Of Set Theory" , Schaum's series, available at archive.org. The author makes concepts very clear.).
– user655689
Mar 25, 2020 at 18:04

• It does use one notation that I consider old-fashioned: $A-B$ for $A\setminus B$. Oct 19, 2014 at 19:29
• What's wrong with $A-B$? Oct 19, 2014 at 20:32
• When $A,B$ are sets of, e.g., numbers, then it is natural to write $A+B=\{a+b\mid a\in A,b\in B\}$. So, @Nishant, what would $A-B$ mean? Oct 19, 2014 at 20:36
• Hmm, that's a good point. The reason I don't like $A\setminus B$ is because I feel like I may write it wrong and/or confuse it with a quotient of $A$ by $B$... Oct 19, 2014 at 20:55