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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Post Your Answer Discard By clicking “Post Your Answer”, you acknowledge that you have read our updated terms of serviceprivacy policy and cookie policyand that your continued use of the website is subject to these policies. Aug 20, Peter rated it really liked it Shelves: 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.

I was one of the first people to sset this answer, and Jaive do agree with what you wrote there. Complicated theories are explained with easy words. Focuses largely on how set theory is used as a basis for modern mathematics, and in particular how to build up a structure with the properties of the natural numbers, including order. None of the concepts within were particularly surprising, but it was good to play with them first-hand.

In some theories this is done. Moreover, every set has more subsets than it has members, so its subsets cannot all be members naife it, although in some instances naiev of them are. The peano axioms can be modeled thfory the the set-theoretic axioms. There are no discussion topics on this book yet. I rushed through and missed a lot of subtleties. Instead, Halmos lets you in on the motivation of why things proceed the way they do, even at the expense of formality.


Naive Set Theory

This is one of my favorite books, ever, even among nonmathematical books. Although it’s focus lies on reading, writing and checking proofs it provides all the necessary information to understand all those proofs.

If you like books and love to build cool products, we may be looking for you. If you’re going to read the book then I suggest reading the whole thing. In my experience, other areas of mathematics are much more fun from a casual standpoint.

Why does this matter? Start by Googling terms like “introduction to propositional logic. Want to Read Currently Reading Read.

I’m reading through the books in the MIRI research guide and will write a review for each as I finish them. No trivia or quizzes yet.

The second is actually quite profound and has not always been believed. Also, there are sef one or two exercises per chapter.

Set theory is axiom soup. Feb 04, Ryan Kirkish rated it really liked it.

Naive Set Theory (book) – Wikipedia

I do not view set theory as foundational. Good introduction to set theory. So the most noticeable thing is that it’s only pages, so I’m assuming there’s a lot it doesn’t cover. 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.

An indexed family is a set, with an index and a function in the background.


Book Review: Naïve Set Theory (MIRI course list)

If you have a background similar to mine, I recommend something a little more advanced. This book contains my answer to that question.

Axiom of choice The axiom of choice lets you, from any collection of non-empty sets, select an element from every set in the collection. I found this book to be rather basic.

The last few chapters were actually a bit too esoteric to finish, I tried. Day to be of great help in getting acquainted with a number of concepts and notations.

I have no point of comparison here. Every mathematician agrees that every mathematician must know some set theory; the disagreement begins in trying to decide how much is some.

Oct 05, Curtis Penner rated it really liked it. It has a laid-back, and even humorous style, which makes it a great pleasure to read. I like the book by E. Normally I’d summarize each chapter, but chapters were about four tiny pages each and the content naiev mostly described by the chapter name.

Book Review: Naive Set Theory (MIRI research guide)

All in all, the book covers lot of ground hallmos a fast clip, and was quite useful. While reading this, keep in mind that I was just reading this to get an overview.

It was nice to examine the actual structure of each type of number in set theory and deepen my previously-superficial knowledge of the distinction.