A Book of Set Theory (Dover Books on Mathematics)

You know Dover-- wonderful for reprinting very high quality texts from back in the 60's or earlier, for 10 bucks US or less, and perfectly adequate for topics that haven't changed since Euclid. But "some" topics, especially those subject to numerical methods, combinatorics and computing, need a makeover to include the web, NumPy, MatLab (or GNU Octave free) and tablet sized supercomputers vs. those era's ideas of computing and combinatorics. This wonderful book gives us the best of both worlds, as the author has graciously updated many areas, such as Russell's paradox (even though it goes back to 1901, let alone 1971!) with additional current set theory paradoxes and current thinking, and many other aspects of set theory and mathematical logic that have become crucial to newer topics like AI, natural language processing, computing, linguistics, combinatorics, the competing category theories, and much more. Even VERY current topics like equivalence in string and M theory use foundation concepts from set theory, so the topic itself is seminal and useful for many fields, from programming to engineering. The book is extremely well written, and quite intuitive (and even fun!) given the dry topic. Although every time I opine that a book requires fairly advanced undergrad I get a bunch of nasty emails from AP High School folks saying they get it, nevertheless, I have to be honest with potential buyers that this IS BOTH a basic (at first), then very advanced text as you proceed. For autodidacts, home schoolers, etc. it makes a wonderful adjunct to the more current texts, as it builds much more gently and intuitively than the majority of "show off" texts today, that expect much more from the reader notation wise. Every author and publisher willing to give as generous a "look inside" as this book does deserves our respect, so do take advantage of it if you're concerned about the level. When you do, you'll see the plentiful diagrams and examples/ exercises that have made this author so popular, for so many decades. If you're old like me, you might "twinge" at the thought of this book, the foundations of which began what was called (and what we were "subjected to") known back then as the "new math." Sets became the transitional pain we endured. Here's the ideal way to make peace with that issue at under 15 bucks! In fact, the author, even back in 71 at the height of it, points out how set theory, in historical perspective, isn't "new" at all, but truly foundational, and as we go forward into topology, rings and even tensors, set theory keeps right up. And if you have a taste for the philosophy of math, indeterminacy, incompleteness, Frege, Godel, uncertainty, and those areas, this is a MUST. Luckily, set theory's "Heisenberg" (Paul Joseph Cohen) published right in this book's wheelhouse, so you'll miss very little by making this choice in that regard. Enjoy!

I work with relational database and while I recently told one of my direct reports that you absolutely DONT need to understand set theory at a level this book goes in to, I'm at that point in my career where the progression of my craft really starts to delve into theories, not just practice. That said, I'm also just a big math nerd. I found Godel Escher Bach (which is laden with logical calculus and set theory, although I didn't know it at the time) to be an amazing bit of work, and while this is far from the esoteric nature of that book, I found myself similarly intrigued by how the author presents the information. It really builds from a basic understanding to give you a solid foundation for stating with confidence how sets will behave, and how you can augment pure set theory as well as apply it creatively.

Excellent. Like the author’s Abstract Algebra book it is a great mix of intuition and detail and just a dash of history. However, the book gets right into the details. This is a plus! But. If you’ve never even *seen* formal logic or set theory it may seem hard to follow. Judging from the written reviews here some people were completely unfamiliar with set theory or formal logic and were lost. That said, for many even by end of freshman year in college, they’ll have seen basic set theory and formal logic presented multiple times. That quick overview that you get for other courses is all you need to jump into this book. But you should get it. If you have no intuition regarding the excluded middle, etc. you may feel lost.

It's definitely a good read. Very straight forward: Here are some definitions, here are some example proofs, I'll show you how to do some and then give you some examples to do, repeat. There was a drawback however. While the books goes into truth tables for propositional logic, and uses them to prove some sentences, it does not give you the actual basic rules of propositional logic. These are rules simply like Modus Ponens, Modus Tollens, Joining, Separation, Weakening, Cases, RAA, contrapositive etc. So essentially what you are going to do is use truth tables for the easier proofs and then use the sentences you've already proved to prove more involved sentences. Which is fine, but I think actually knowing the rules of propositional logic make proving these sentences and understanding the actual set theory much more intuitive. There are also some typos in the book, even in a theorem I noticed: Theorem 1.27 of unordered pairs should be If {x,y} = {u,v} then [x = u and **y = v**] or [x = v or y = u]. The typo is where I put the ** as the book says y = u instead of y = v. Anyways, I'm still giving it 4 stars simply because I say it's worth getting if you want to jump into set theory and its a lot better than some other set theory books I read.

I am a mathematics professor, but needed to brush up on a few facts about cardinal and ordinal numbers from set theory, that I never formally learned in any of my courses in graduate school. This book was written at a good level for me to quickly learn what I needed. The early part of the book is very elementary and it the kind of stuff that is taught at my university to freshman math majors. But some of the later chapters actually have a bunch of the set theory that never seems to be taught unless you actually take a course called "set theory". I bought both the paper version and the Kindle version. The paper version is very good, but the Kindle version sometimes does not display formulas correctly.

Livro excelente, faz NGB numa linguagem informal misturando com símbolos mathemáticos usuais e familiar a qualquer estudante de matemática, física ou áreas afins. Recomendo bastante! Excellent book, makes NGB in an informal language mixing with usual math symbols that are familiar to any student of math, physics or related fields. I strongly recommend.

Pretty high level.

This book is great. Complete delight. However I am upset with Amazon, as you can't read this book in kindle device. It works fine in Kindle app. In kindle device one line results, formulas, deductions, mostly in very very tiny fronts, and in most of the cases you can't enlarge it. So reading the book in kindle device is really really painful. Amazon need to rectify this.

This book is aimed at final year students and graduates. It is not suitable for those who wish to learn the basics of set theory. The book comprehensively covers axiomatic set theory and shows how, in a formal manner, the theory leads to the axiomatisation of the number system and other fields of mathematics. The book has lots of exercises to test your knowledge.

This is a really fine book for a first course in Set Theory. It touches just about every important topic with a nice balance between rigor and clarity. It might be a bit advanced to be the main text at a small institution like mine (we have to reach a wide audience in a single one-semester course). But, if I teach the course again, I shall definitely use it as a secondary text and will encourage students to purchase the Kindle edition. I have known of the book for a long time and now wish I had read it in detail many years ago. Kindle provides an important service by making good older books like this available at a reasonable cost.