Elements of set theory

What Hacker News says

1. openasocketMar 2024
   For any f and A, we can define X as { a in A | a is not in f(a) } . That set exists in ZFC by the axiom of separation, also known as the axiom of subsets or the axiom of comprehension.

   I recommend you pick up a book on ZFC if you are interested in understanding set theory. I found Enderton’s “Elements of Set Theory” to be a really good introductory text.

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2. blindmuteMay 2022
   In order:

   1. Book of Proof

   1a. How to Prove It: A Structured Approach

   2. Elements of Set Theory - Enderton

   2a. Naive Set Theory - Halmos

   3. Foundations of Analysis - Landau

   4. Basic Mathematics - Lang

   5. Principles of Mathematics - Allendoerfer & Oakley

   6. A Transition to Advanced Mathematics

   6a. Concept of Modern Mathematics - Stewart

   7. Calculus - Apostol or Spivak

   Don't skip any

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3. jessupJun 2015
   "Elements of Set Theory" by Herbert B. Enderton....

   ℝ ≈ P(ℕ)

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4. joewferraraSep 2023
   I’m not sure about textbooks specifically on infinity. As another comment mentions, the study of infinity generally falls under the math subject of set theory so a set theory textbook would be a mathematician’s definitive resource on infinity. I learned set theory from the book Elements of Set Theory by Herbert Enderton. I’d say that books alright, but would not give it my highest recommendation. It’s very dry and technical, and most of it’s not about infinity.
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5. poletopoleApr 2021
   I've been hunting for a quality textbook on elementary set theory for about a year without much success. What I'm looking for is a modern text that covers subject matter from first principles save perhaps logic. Out of the many books I looked at I bought the following three:

   1. "Set Theory: A First Course" by Daniel Cunningham: this book is a good reference book but makes too many assumptions to teach yourself set theory. I actually had to buy this one twice since Amazon didn't deliver the first!

   2. "Elements of Set Theory" by Herbert Enderton: This book is actually not too bad and I may have to default to it if I find nothing better. This book however is ancient and I'll have to buy a physical copy because the math symbols were drawn before TeX was invented.

   3. "Naive Set Theory" by Paul Halmos: This book was complete garbage hands down, no more needs to be said.

   In addition to those three books, there were many that obviously were either too brief in coverage of the subject matter and assumed much too fast or I was unable to find previews in able to judge their quality and thus decided against the gamble to buy.

   Is set theory even taught in college? I've been through the major educational publisher's catalogs and couldn't find anything on set theory other than #1 from Cambridge. The best book so far wasn't even about set theory, it was MIT's phonology textbook by Bale and Reiss (which I highly recommend, easily one of the best textbooks I've ever come across).

   If set theory really is the foundation of modern mathematics you would think there would be a decent textbook on the subject. I would have posted this question to math.stackexchange but what I've learned is that, at least for mathematicians, seem to recommend either books that are arcane, obscure, or are way too advanced to be useful for the user whom is asking the question.

   So HN, I'm desperate and could use any recommendations offered, thanks!

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