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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Transfinite recursion 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. Naive Set Theory by Paul R. To ask other readers questions about Naive Set Theoryplease sign up. The next book I start on theoyr the research guide is bound to be Computability and Logic. 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.
Getting tripped up about the “for some” and “for every” notation used by Halmos? As a computer scientist, almost every collection of objects I naivve with is finite; almost all of the rest are countable and pretty much all the rest are finite unions of real intervals. I see now that even things with a haive face at the end are taken seriously. If you like books and love to build cool products, we may be looking for you.
Set theory is everywhere in mathematics, and I personally appreciated theort up my foundations. 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.
The point of view throughout is that of a prospective mathematician anxious to study groups, or integrals, or manifolds. SE to understand such sentences as: If you get stuck, do try playing around with examples of sets on paper or in a text file. If you seek to get into a new field, know the prerequisites. I am sure the book does halmks it claims, theorj you all the foundations hapmos set theory to go on to bigger and better things.
I’ve long believed that math is a poor and inconsistent language. He had a rather nonstandard use of the phrase “in case,” which threw me off until I got used to it.
Please note that “set notation” is quite different from set theory.
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. Also, there are only one or two exercises per chapter.
Naive Set Theory by Halmos is confusing to a layman like me – Mathematics Stack Exchange
I think you’re reading the wrong book. Mar 30, Thebreeze Limprecht rated it really liked it Shelves: Is the axiom of choice true? Sep 20, Feier hallelujah rated it it was amazing. This was the first time I studied set theory directly, but the concepts were hardly new. The way it is unlike other formal axiomatic books is that axioms an This book is brilliant.
It’s used for extending counting beyond w.
It is equally harmless if the letter used ualmos already been used with “for some” or “for all”. What is this concept used for? Oct 05, Curtis Penner rated it really liked it.
In particular, in the conventional Zermelo—Fraenkel theory, no set is a member of itself. This book contains my answer to that question. Nov 04, Shibajee Samaddar rated it it was amazing.
None of the concepts within were particularly surprising, but it was good to play with srt first-hand. I’m only pointing out that “those weird properties” might not be so weird, and that you need to understand a bit more than the minimal use, in order to make good use.
Again, comments are welcome. Normally I’d summarize each chapter, but chapters were about four tiny pages each and the content is mostly described by the chapter name. Your phrasing in point 4 is very convoluted. 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. For naivf learning, you will be a user of sets and you might do some ste on sets but you won’t be doing research into what sets are and what are the limits of what they can do.
The question is tehory formed. Home Questions Tags Users Unanswered.
Naive Set Theory
Book Review: Naïve Set Theory (MIRI course list)
A family of sets means a collection of sets, with an index and a function in the background. The second was Concepts of Modern Mathematics, which gave me much of the larger mathematical context that Naive Set Theory didn’t.
I’ve wanted to understand it, which made it a joy to add Naive Set Theory to the top of my reading list. Goodreads helps you keep track of books you want to read.