I'm planning to buy a book about the axiom of choice. Would you recommend any in particular, and if so, why?

If I were to give you a list of books, how would you go about deciding which one to read?

What do you mean by 'axiom of choice'?

I'm planning to buy a book about the axiom of choice. Would you recommend any in particular, and if so, why?

I hope my advice suffices.

I'm planning to buy a book about the axiom of choice. Would you recommend any in particular, and if so, why?

The axiom say there is a choice function F for a set X of non-empty sets s .
If X is finite, and the sets in X in finite, then There is an enumerable number of such F. Surely, such F exist, but the problem shift to uniqueness. Which one is it? On the other hand, for the sets in X that might be infinite. You can ` t enumerate it, so that can be a problem.

simple case:

X= { {0, 1}, { 2, 3}}

has 4 candidate for F. They are { (0, 2), ( 0, 3), ( 1, 2), (1, 3)}.

while X= { N, C}

N is the natural numbers,

and

C is the complex numbers.

if we say:

1. { (x, y) | x in N, y in C}

This would solve the problem of existence( but not uniqueness), but 1 commit us to infinite sets.

The statement of the problem largely suppose existence of infinite sets, so i think the axiom of choice is largely to do with uniqueness, and not existence. They are separate questions.

Ughaibu may be asking for a book rather than an answer. What is the name of the book that you draw this information from so that Ugaibu can look into it?

A good, non-technical history is Gregory H. Moore, Zermelo's Axiom of Choice: Its Origins, Development, and Influence (Springer 1982). I know I enjoyed reading or skim-reading it, but I'm afraid I can't remember in detail what I thought of it. Also, it's out of print

A more technical treatment, recently republished by Dover as a cheap paperback, is Thomas J. Jech, The Axiom of Choice, but I'm afraid I haven't read it.
The Axiom of Choice

Thanks. Unfortunately it's priced in the fantasy range.
Zermelo's Axiom of Choice: Its Origins, Development, and Influence: Amazon.ca: G.H. Moore: Books
I considered that and Amazon.com: The Axiom of Choice (Studies in Logic Series) (9781904987543): John L Bell: Books I suspect, none exactly meets my fussiness. Anyway, I'll report on the Herrlich book, after it arrives.

I would appreciate your sharing your thoughts on it. In which section should I expect to see your post?

Actually sometimes they'll buy books you recommend... as I recall.

I'll post on this thread.I will be very surprised if I can talk a Japanese library into buying an obscure maths book, written in english, but, maybe I'll give it a go.

I'm planning to buy a book about the axiom of choice. Would you recommend any in particular, and if so, why?

Being a Five means always needing to learn, to take in information about the world. A day without learning is like a day without 'sunshine.

They believe that developing this niche is the best way that they can attain independence and confidence.

Thus, for their own security and self-esteem, Fives need to have at least one area in which they have a degree of expertise that will allow them to feel capable and connected with the world.

I always thought free will, & determinism is what you are fixed on.

Strange, what's your explanation for all my battles against JTB?

INTPs are relatively easy-going and amenable to almost anything until their principles are violated, about which they may become outspoken and inflexible. They prefer to return, however, to a reserved albeit benign ambiance, not wishing to make spectacles of themselves.