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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This is one of the smallest books Haomos have, at only pages. Halmos is using some dated terminology and is in my eyes a bit inconsistent here.

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. Most of these throry are small compared to the amount of good data in the book. Zorn’s Lemma states that if all chains in a set have an upper bound, then the set has a maximal element. 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.

Naive Set Theory

This book seems well-suited for a layperson interested in learning set theory. You can try with: How does it fit in to the larger subject of mathematics? It has been said that everything on the internet that is said without a smiley face at the end will be taken seriously.

Just like everybody who uses mathematics just assumes that the real numbers exist and have the obvious properties. Can you be a theoretical mathematician and make a B in Calc I approximately the third time anive took it? Read this chapter before Cardinal arithmetic. I am at the same time humbled by the subject and empowered by what I’ve learned in this episode.


Aug 20, ‘Asem Ismaiel rated it liked it. If you do have a somewhat fitting background, I think this should be a very competent pick to deepen your understanding of set theory. Fred Conrad rated it really liked it Jan 14, It builds from first principles up to cardinality, and nothing hamos the way is unimportant. Transfinite recursion is an analogue to the ordinary recursion theorem, in a similar way that transfinite induction is an analogue to mathematical induction – recursive functions for infinite sets beyond w.

A confusing way of talking about sets. Just a moment while we sign you in to your Goodreads account. Start by Googling terms like “introduction to propositional logic.

An indexed family is theogy set, with halmod index and a function in the background. Can anyone recommend a better introduction to informal set theory than Halmos? In particular, essentially all the objects you’ll come across that you might want to describe as “sets” will be subsets of something that definitely is a set, such as the integers.

I think you’re reading the wrong book. 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 feel the author is a bit wordy at times. Complements and powers The axiom of powers allows one to, out of one set, create a set containing all the different possible subsets of the original set.

It’s a very rudimentary treatment on set theory that is more verbose than other books on the topic. Some help on the way: I think Naive Set Theory wasn’t the optimal book for me at the stage I was. Every page is a conundrum that requires huge amounts of mental gymnastics.

Naive Set Theory (book) – Wikipedia

No trivia or quizzes yet. Arithmetic The principle of mathematical induction is put to heavy use in order to define arithmetic. I’m extremely surprised you never came across it before given that you’ve taken courses in, e. This extra condition is useful when working with infinite sets.


I can imagine that that would require some actual set theory. 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. Sign up using Email and Password.

A bit into the book, I started struggling with the exercises.

It seems that this is a thepry rope to walk for other authors, and sett guy did it right. Final Notes If a comparably short-and-sweet textbook written in the last twenty years can be found, I recommend updating the suggestion on the MIRI course list. Would I recommend it as a starting point, if you would like to learn set theory? Families This chapter tripped me up heavily because Halmos mixed in three things at the same time on page In modern lingo, what Halmos calls a “similarity” is an “order isomorphism”.

Oct 07, Julia rated it it was amazing Shelves: Please note that “set notation” is quite different from set theory. Cantor’s halnos states that every set always has a smaller cardinal number than the cardinal number of its power set. I like the book by E.

They would resort to “for some” or “for any” in largely english-language proofs.

Naive Set Theory by Paul R. Halmos

Summary Is it a good book? Books by Paul R. The high school didn’t teach any theoretical foundation of math at all.

You don’t read math book like you read a novel. Puzzled by the bit about Russell’s paradox at the end of the chapter? Is the axiom of choice true?