does the sticky recomend meme books? where can I get a proper

>>9001855
the sticky is shit
naive set theory by halmos is good, the first chapters of jech's set theory are harder but great

>>9001855

yes.

pick yourself up a discrete mathematics books or something of the sorts.

How to Prove It, is a great book for supplement.

>>9001855
>set theory is literally the foundation of all other mathematics
>what is category theory

>>9001857
>>9001856
I meant to ask why does it?

that pic is from elements of set theory and quite frankly that proof is shit.
>>9001856
thanks anon for the book reccomendation
>>9001858
category theory is too detached from application

>>9001858
the definition of a category has the word set in it
you double nigger

Naive Set Theory always gets recommended but I think it's shit for anyone who doesn't already know and understand the subject. It's as dense as could be. Try The Foundations of Mathematics by Ian Stewart and David Tall instead

>>9001870
No it doesn't.

>>9001856
I'm just going to second this recommendation. Halmos's book is all the set theory a mathematician ever needs to know, Jech's book is good if you have a deeper interest in set theory as a field of math (you can decide on this after reading Halmos's book).

>>9002229
>a category consists of a class of objects and a set of morphisms
>set of morphisms
>set

>>9002254
The collection of morphisms is not a set unless the category is locally small.

>>9001855
http://4chan-science.wikia.com/wiki/Mathematics#Proofs_and_Mathematical_Reasoning
http://4chan-science.wikia.com/wiki/Mathematics#Set_Theory.2C_Mathematical_Logic.2C_and_MetaMathematics

>>9001855
There are a few things you should be aware of if you want to learn proper (non-wishy-washy) set theory:

>Most people only work with a small subset of set theory. For this it is sufficient to know something called "Naive Set Theory". This is by definition wishy-washy set theory. Essentially it teaches a bunch of basic definitions and concrete analogies to give you a feel for some basics of set theory. Unfortunately it isn't given with an axiomatic system and thus is what is called "not even wrong" (i.e. it's not even rigorous enough to argue that it's wrong).
>The problem of defining an axiomatic system for Set Theory was a difficult one and there were lots of solutions (many of them wrong or equivalent). There were even alternatives like type theory and wildly different sorts of "Set Theories".
>The "standard" variation is ZFC Set Theory but when you get down to the nitty-gritty there are actually a few different axiomatic systems for it. This means that resources on ZFC are often not interchangable (e.g. if you hit a snag in a book it isn't always possible to look up more information in another book or online as the systems may differ).

(cont.)

>>9002909

>The C in ZFC refers to a controversial axiom called the Axiom of Choice. There are many equivalent axioms for it. It is an extremely powerful axiom that is added in order to make "infinite sets" behave nicely like collections. There is some opposition to this, in particular some argue that "sets" are really abstract mathematical objects and we only "think" of them as collections to make it easier to wrap our heads around them. Without Choice (i.e. in ZF) you get a lot of different and incompatible definitions for an infinite set (I've seen upwards of 8) and these infinite sets exhibit all sorts of interesting behavior that doesn't relate well to real world analogies. Choice on the other hand also introduces its own share of bizarre behavior like the Banach Tarski paradox. Another criticism of choice is that proofs that use it are non-constructive (that is to say they are indirect and make use of double negations), as such one should avoid it whenever possible (i.e. when not explicitly working with infinite sets) and make note of its use otherwise.
>NBG Set Theory is very different and also popular. This set theory introduces the notion of objects called classes. It is often the sort of Set Theory used when dealing with topics like Category Theory.
>Many books on ZFC actually spend much of their time developing mathematical foundations. That is defining each of your sets of numbers and arithmetic operations in full formalism. In other words, they don't really teach you Set Theory so much as they teach you Introductory Foundations.

(cont.)

>>9002911

Halmos book is the best Naive Set Theory book out there and probably the best place to start.
I have read many axiomatic Set Theory books and each one has its own share of major problems. I can recommend no books.

>>9002873
The sticky is shit.

>>9001858
>>9002259
I'm not that guy but while category theory is great, there aren't many books or resources out there that teach it purely without requiring a bunch of background in set theory and other mathematics (for instance, try defining locally small without requiring the notion of a set). There are a few good resources that do it from a comp sci perspective but in doing so they then require some background in type theory or at the very least experience with a functional programming language like Haskell.

Moreover, not everything can be done with raw category in an intuitive way (many constructions of basic things feel weird and contrived to the average reader).

>>9002912
>(many constructions of basic things feel weird and contrived to the average reader).
t. bourbakian wanabee

CT for the sake of CT is the best