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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Book Review: Naïve Set Theory (MIRI course list)

Consequently, while reading Naive Set Theory, I spent at least sdt much time reading other sources! I’m reviewing the books on the MIRI course list.

Please note that “set notation” is quite different from set theory. Most useful was interacting with ordinal and cardinal numbers. The purpose of the book is 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.

If you’re going to read the book then I suggest reading the whole thing. Is the axiom of choice true?

Numbers The axiom of infinity states that there is a set of the natural numbers. I have no point of comparison here.

As a computer scientist, almost every collection of objects I deal with is finite; almost all of the rest are countable and pretty much all the rest are finite unions of real intervals. Ordered pairs Cartesian products are used to represent plenty of mathematical concepts, notably coordinate systems. Set theory is more mature now than it was then. Order Partial orders, total orders, well orders — are powerful mathematical concepts thory are used extensively.

This was the first time I studied set theory directly, but the concepts were hardly new. In my opinion it manages to keep the language simple and aids students to find their way by pointing out important caveats.

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Build your knowledge in solid steps. Functions Halmos is using some dated terminology and is in my eyes a bit thdory here.

This is pretty much what is done every time set builder notation is employed. The s feel is definitely fun.

Naive Set Theory by Halmos is confusing to a layman like me – Mathematics Stack Exchange

Good introduction to set theory. I like the book by E. The proofs given were primarily in english. One of the most beautiful sources of set-theoretic wisdom is still Hausdorff’s Set theory.

Naive Set Theory

But then again I am not really a math person. Since you have found your way into Stack Exchange, then theorh have access to quality help when your brain starts melting due to overload. Replace Halmos’ “onto” with surjective, “one-to-one” with injective, and “one-to-one correspondence” with bijective. I am not familiar with machine learning, but I doubt that it requires set theory. I have a number of loose ends to tie up before jumping in to Model Theory, and I have much less familiarity with the subject matter.

Instead, Halmos lets you in on the motivation of why things proceed the way they do, even at the expense of formality.

The author shows you the nuts and bolts of set theory and doesn’t waste any time doing it. I rushed through and missed a lot of subtleties.

A family of sets means a collection of sets, with an index and a function in the background. Yes, I’m assuming all of those things. Muhammad Kalvianto rated it really liked it Feb 16, Only a few exercises are designated as such since the book itself is an ongoing series of exercises with hints.

So you’re essentially taking more than you claim to have taken. The author also seemed to sprinkle in elements of a dry sense of humor, which in no way detracted from the delivery of the content. I was one of the first people to vote this answer, and I do agree with what you wrote there. What should I read? Conversational and light hearted, it makes learning of the basics of set theory a joy.


Jan 01, Vincent Russo rated it really liked it Shelves: They would resort to “for some” or “for any” in largely english-language proofs. To build a solid foundation in proofs, I will now go through one or two books about mathematical proofs. Discussion Before diving in to the review it’s important to remember that the usefulness of a math textbook is heavily dependent upon your math background.

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. This book seems well-suited for a layperson interested in learning set theory.

You’d better get used to it: I wouldn’t be surprised if it’s not, but I don’t know. 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.

I majored in biology and attended calculus, statistics, real analysis, and linear algebra classes in a university. Cardinal arithmetic is an arithmetic where just about all the standard operators do nothing beyond the finite cases. It’s a very rudimentary treatment on set theory that is more verbose than other books on the topic.

I know that I shouldn’t expect better, but one can dream. Different if they do not. Did a Directed Reading Program with an undergraduate interested in logic with this book.