A Book of Set Theory (Dover Books on Mathematics) by Charles C Pinter (PDF)

Description

Suitable for upper-level undergraduates, this accessible approach to set theory poses rigorous but simple arguments. Each definition is accompanied by commentary that motivates and explains new concepts. Starting with a repetition of the familiar arguments of elementary set theory, the level of abstract thinking gradually rises for a progressive increase in complexity.A historical introduction presents a brief account of the growth of set theory, with special emphasis on problems that led to the development of the various systems of axiomatic set theory. Subsequent chapters explore classes and sets, functions, relations, partially ordered classes, and the axiom of choice. Other subjects include natural and cardinal numbers, finite and infinite sets, the arithmetic of ordinal numbers, transfinite recursion, and selected topics in the theory of ordinals and cardinals. This updated edition features new material by author Charles C. Pinter.

User’s Reviews

Editorial Reviews: From the Back Cover Suitable for upper-level undergraduates, this accessible approach to set theory poses rigorous but simple arguments. Each definition is accompanied by commentary that motivates and explains new concepts. Starting with a repetition of the familiar arguments of elementary set theory, the level of abstract thinking gradually rises for a progressive increase in complexity.A historical introduction presents a brief account of the growth of set theory, with special emphasis on problems that led to the development of the various systems of axiomatic set theory. Subsequent chapters explore classes and sets, functions, relations, partially ordered classes, and the axiom of choice. Other subjects include natural and cardinal numbers, finite and infinite sets, the arithmetic of ordinal numbers, transfinite recursion, and selected topics in the theory of ordinals and cardinals. This updated edition features new material by author Charles C. Pinter.Dover (2014) revised and corrected republication of Set Theory, originally published by the Addison-Wesley Publishing Company, Reading, Massachusetts, 1971.See every Dover book in print atwww.doverpublications.com About the Author Charles Pinter is Professor Emeritus of Mathematics at Bucknell University and the author of Dover’s highly successful Book of Abstract Algebra.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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!

⭐There are many good books out there on Set Theory, and I have consulted many of them. This one explains things very clearly and succinctly, and I found it to be an excellent source. I am am studying Set Theory on my own, and a text of this caliber has been very helpful.I’ve used this to help understand Set Theory, an Intuitive Approach, by You-Feng Lin. Also have used Scahum’s Set Theory.

⭐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.

⭐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.

⭐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.

⭐This is a great intro book on set theory, especially as it follows Goedel-Bernays rather than the more usual ZF prioritization. As others have pointed out, there are quite a few typos in the text to trap the unwary. But the real problem lies in the use of what must be two point fonts for theorems and examples, making them essentially unreadable. Granted, you can select them and call up a zoomed out-of-book display which must be dismissed in order to go back and see the formula in context, a process which can take a number opposes at the X in the upper right corner. Sometimes, for an inline formula, the displayswitches mid-formula to the extremely small font. This seems like it should be easy to fix. And doesn’t anyone proof read these before they are offered for sale as Kindle books? Perhaps Amazon should fix these and offer free upgrades to these broken books. It is a common problem with Kindle technical books.

⭐A must have book for anyone wanting to improve his/her knowledge of the subject. Anyone aspiring to understand anything related to maths should read a book like this first.

⭐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.

⭐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.

⭐Der Autor schreibt in seiner Widmung “To my students, from whom I have learned how to explain and how to teach”. Diesen “Spirit” spürt man in dem ganzen Buch. Saubere Definitionen und klare Erläuterungen, warum man das so und so macht und nicht anders. Ganz im Geiste des Klassikers “Halmos – Naive Set Theory”. Die Lektüre kann ich nur sehr empfehlen.

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⭐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.

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