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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The book has a terse presentation which makes it tough to digest if you aren’t already familiar with propositional logic, perhaps set theory to some extent already and a bit of advanced mathematics in general.
See in particular this article: Is it a good book? 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 logic Every mathematician agrees that every mathematician must know some set theory; the disagreement begins in trying to decide how much is some. Families are an alternative way of talking about sets.
The takeaway is that the book was good, but likely could have been better in light of modern mathematics. I think Halmos’ Naive Set Theory is primarily concerned with set theory as a foundation on top of which mathematics is built, but the word “naive”, if I understand correctly, just means he’s viewing the concept of a set concretely eet a collection of things rather than axiomatically as being whatever satisfies the axioms.
Any further questionsI am happy to answer: Some specific subjects analysis, type theory, group theory, etc. In programming languages, you tend to have to be thory more 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.
Axiomatic Set Theory by Suppes, as far as I remember, had nothing of the sort. Go back to your old boss, and tell him that if you read the whole book, you accomplish “reading the entire thing”. As the author explains in the introduction, it means that he takes a somewhat informal approach to axioms and proofs, but as also yalmos in the introduction, the book is axiomatic in that he does state axioms and use them in subsequent proofs. One of the most beautiful sources of set-theoretic wisdom is still Hausdorff’s Set theory.
Naive Set Theory (book) – Wikipedia
Seriously, make sure you understand first-order logic. My only suggestion is that you swap chapter 25 and There are very few displayed theorems; most of the facts are stated in simple terms, followed by a sketch of the proof. A recent and highly readable addition to nxive literature, with an extensive and up-to-date bibliography, is Axiomatic set theory by Suppes. 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.
I think Naive Set Theory wasn’t the optimal book for me at the stage I was. Derek Goldrei, Classic set theorybut some “practice” with mathematical and logic symbolism is needed There was little exploration of each axiom, what it cost and what it bought, and what alternate forms are available.
Which is to tehory, the book won’t dig to the depths of formality or philosophy, it focuses on getting you productive with set theory.
Naive Set Theory by Paul R. Halmos
None of the concepts within were particularly surprising, but it was good to play naiev them first-hand. All this stuffyou will encounter while studying MLso better to be comfortable beforehand.
I’m not advocating for the Naice to sit and plow through Jech and Kunen, or even through all of Halmos’ book. This is more than you claim in your answer, and the difference is exactly where understanding Russell’s paradox. Day to be of great help in getting acquainted with a number of concepts thfory notations.
It is a glimpse of how mathematics, and mathematicians, work. Muhammad Kalvianto rated it really liked it Feb 16, Better questions are shaped like “does the axiom of choice apply to this thing I’m working with?
The first chapter of any undergrad textbook on general discrete mathematics will almost certainly contain all the set theory you need for machine learning. Ordered pairs Cartesian products are used to represent plenty of mathematical concepts, notably coordinate systems.
The way it is unlike other formal axiomatic books tueory that axioms and proofs are not simply stated distilled down to their final concise and often incomprehensible form.
Book Review: Naive Set Theory (MIRI research guide)
Arda rated it really liked it Mar 31, Sets are the same if they contain the same elements. I found this book to be rather basic. In math, you can freely express something like “Out of all possible x evergive me the set of x that fulfill this condition”. On pagesI encountered if and only if and had to go to Wikipediato actually understand it.
Oct 05, Curtis Penner rated it really liked it. Functions Halmos is using some dated terminology and is in my eyes a bit inconsistent here. All in all, the book covers lot of ground at a fast clip, and naiev quite useful.
Good introduction to set theory.