You are ready. You don’t read math book like you read a novel. You can literally spend days on one page. You are not going to find a better book than Halmos’s. Every mathematician agrees that every mathematician must know some set theory; the Naive Set Theory. Authors; (view affiliations). Paul R. Halmos. Book. Every mathematician agrees that every mathematician must know some set theory; the disagreement begins in trying to decide how much is some. This book.
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Goodreads helps you keep track of books you want to read. Want to Read saving…. Want to Thsory Currently Reading Read. Refresh and try again. Open Preview See a Problem? Thanks for telling us about the problem. Return to Book Page. Naive Set Theory by Paul R. Every mathematician agrees that every mathematician must know some set theory; the disagreement begins in trying to decide how much is some. This book contains my answer to that question. The purpose of the book naiv to tell the beginning student of advanced mathematics the basic najve theoretic facts of life, and to do so with the minimum of philosophical discourse and logic Every mathematician agrees that every mathematician must know some set theory; the disagreement begins in trying to decide how much is some.
The purpose of the book theogy to tell the beginning student of advanced mathematics the basic set- theoretic facts of life, and to do so with the minimum of philosophical discourse and logical formalism. The point of view throughout is that of a prospective mathematician anxious to study groups, or integrals, or manifolds.
From this point of view thery concepts and methods of this book are merely some of the standard mathematical tools; the expert specialist will find nothing new here. Scholarly bibliographical credits and references are out of place in a purely expository book such as this one.
The student who gets interested in set theory for its own sake should know, however, that there is much more to the subject than there is in this book.
One of the most beautiful sources of set-theoretic wisdom is still Hausdorff’s Set theory. A recent and highly readable addition to the literature, with an extensive and up-to-date bibliography, is Axiomatic set theory by Suppes.
Hardcoverpages. Published January 16th by Springer first published To see what your friends thought of this book, please sign up. To ask other readers questions about Naive Set Tehoryplease sign up. Lists with This Book. May 09, Meysam Ganji rated it it was amazing.
Book Review: Naive Set Theory (MIRI research guide)
Dec 15, Tyler McMann rated it it was amazing Shelves: This is one of my favorite books, ever, even among nonmathematical books. Paul Halmos is often held up as a paragon of mathematical writing, and reading this book one can see why.
It has a laid-back, and even humorous style, which makes it a great pleasure to read. The Axiom of Choice is introduced in the way that the founders of set theory first saw it, as a guarantee that the Cartesian Product of two nonempty sets is nonempty, and is developed into its modern form.
The book ends simply with th This is one of my favorite books, ever, even among nonmathematical books.
Book Review: Naïve Set Theory (MIRI course list)
The book ends simply with the statement of the Continuum Hypothesis. This is one of the smallest books I have, at only pages. Instead of chapters it has sections, each between three to five pages long, with 25 sections in total. While it may seem small, it can take a surprising amount of time to read it, due to the confusing nature of set theory itself.
Sep 10, Bryce Woodworth rated it really liked it Recommends it for: Good introduction to set theory.
Pretty terse in terms of proofs, leaving a lot of steps up to the reader, which I like. Each section is only about 2 pages, but manages to cover a good amount of intuition. Focuses largely on how set theory is used as a hwlmos for modern mathematics, and in particular how to build up a structure with the properties of the natural numbers, including order.
Set theory is vital to know in modern mathematics, but you almost certainly don’t need the level of depth this Good introduction to set theory. Set theory is vital to know in modern mathematics, but you almost certainly don’t need the level of depth this book goes into for day-to-day work.
Still, it is interesting and a fun read for the curious. Mar 16, Basel Al-Dagen rated it it was amazing. I was going to give the book a 4 stars rating,but since in the book cover the book contain itself,it totally made it a hard 5. This book is brilliant. It is so much more than a math halmks.
It is a glimpse of how mathematics, and mathematicians, work. As the author explains in the introduction, it means that he takes a somewhat informal approach to axioms and proofs, but as also stated in the introduction, the book is axiomatic in that he does state axioms and use them in subsequent proofs.
The way it is unlike other formal axiomatic books is that axioms an This book is brilliant. The way it is unlike other formal axiomatic books is that axioms and proofs are not simply stated distilled down to their final concise and often incomprehensible form. Instead, Halmos lets you in on the motivation of why things proceed the way they do, even at the expense of formality. For example, he spends the second last chapter giving you the rules of cardinal number arithmetic before even defining them in the last chapter — that comes in the last chapter, but not before he explains why we chose that definition among other alternatives.
These motivating passages are actually less frequent than I would have liked, but they do enough to motivate not only specific definitions, but to motivate what the axiomatic set theory approach is all about.
What I got out of it is that set theorists aim to find definitions of intuitive, self-evident concepts using the bare minimum of new constructions. In some theories this is done.
Naive Set Theory by Halmos is confusing to a layman like me – Mathematics Stack Exchange
He can even be quite humorous at maive — I laughed out loud reading a passage on page Nov 04, Shibajee Samaddar rated it it was amazing. Naiv 20, Feier hallelujah rated it it was amazing. Complicated theories are explained with easy words.
The exercises are useful too. Oct 05, Curtis Penner rated it really liked it. Even though the book is thin, the subject is thick. When finished the read should have a better understanding of Set Theory. Apr 17, Jonathan rated it really liked it. While reading this, keep in mind that I was just reading this to get an overview.
I rushed through and missed a lot of subtleties. So the most noticeable thing is that it’s only pages, so I’m assuming there’s a lot it doesn’t cover. Though I’d imagine a lot of the shortness comes also from being naive set theory, rather than a fully rigorous treatment of axiomatic set theory.
Also, there are only one or two exercises per chapter. The best part was the minor bits of contextual information. We only include it to show how ordered pairs come from sets and will not reference it again.
Axiomatic Set Theory by Suppes, as far as I remember, had nothing sett the sort. I feel the author is a bit wordy nzive times. He had a rather nonstandard use of the phrase “in case,” which threw me off until I got used to it. Though for all I jalmos, that’s the normal way for mathematicians srt use that phrase.
So in conclusion, if you want to really dig into the subject, I’d recommend something more like Suppes’ Axiomatic Set Theory instead, though Naive Set Theory is certainly an excellent supplement. Oct 15, David Lindelof rated it it was amazing. A just amazing little book of about pages which explains the fundamental principles of set theory, and which shows how, from these principles, one can derive the concept of natural numbers and therefore the rest of mathematics.
I should also mention that it is only after reading this book that I realize how wrong I was in my idea of tbeory a ‘relation’ in ‘relational database’ meant. Jan 01, Vincent Russo rated it really liked it Halmls I stumbled on this book my accident, and gave it a read. It’s a very rudimentary treatment on set theory that sset more verbose than other books on the topic.
The author also seemed to sprinkle in elements of a dry sense of humor, which in no way detracted from the delivery of the hxlmos. It seems that this is a tight rope to walk for other authors, and this guy did it right. Aug 20, Peter rated it really liked it Shelves: Really nothing too “naive” about it. The last few chapters were actually a bit too esoteric to finish, I tried.
But then again I am not really a math person.
I am sure the book does what it claims, gives you all the foundations in set theory to nqive on to bigger and better things. It did more than enough for me, even without the last few chapters. Jul 10, Santino Maguire rated it it was ok. This text shows its age — it’s heavily wordy and pretty light on presenting things in mathematical notation. Although I have never formally studied set theory, I didn’t get much out of it, though halos did serve to reinforce my knowledge of some of the algebra behind sets.
Nov 03, Noah Hughes rated it it was amazing. Fheory excellent introduction for someone just coming to the ideas of set theory. Conversational and light hearted, it makes learning of the basics of set theory a joy. Did a Directed Reading Program with an undergraduate interested in logic with haive book.
Feb 19, S marked it as to-read Shelves: Man, even though I’m hardly disciplined enough to put fuel in my car, I’m still head over heels with rigorous Mathematics and Sets.