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I study CS, but on the first semester I have a lot of mathematics. Of course, there is an introduction to set theory and logic. Recently, we had lectures about cardinality, different kinds of infinity, countable sets etc. I know the basics, but I don't understand many ideas as I would like to understand them.

Well, I am looking for a book/article/tutorial/etc. which is a good explanation of cardinality, countable sets, idea of different kinds of infinity and cardinality of sets of different functions. Now, I only need sources, which cover the basics, but I don't mind if You post something on higher level (but introduction stuff has greater priority).

PS: I was looking for similar questions on this site, I've found for exaple [1] and [2], but it isn't what I'm actually looking for.

I woluld appreciate You help.

[1] Cardinality of set of real continuous functions

[2] Different kinds of infinities?

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6 Answers

If you don't mind relatively high level reading (though it starts from the basics, you just need to be able to even read mathematical texts):

Introduction to Cardinal Arithmetic

The preface and first chapter is about introduction to cardinal arithmetic, you probably don't need it all, but there's a good introductory part there.

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This is at least the fifth time I have posted this on this site. But it is free, so here it comes again:

I have some relatively brief notes on introductory set theory available on my webpage. Please go to

http://www.math.uga.edu/~pete/expositions.html

and scroll most of the way down to the bottom. Or more directly go this page:

http://math.uga.edu/~pete/settheorypart1.pdf

If you get to the end of these notes and are still curious, try replacing the "1" by a "2", and so forth. But in particular the first set of notes is intended to be used by undergraduates with absolutely no prior background in set theory.

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I like Devlin's "Joy of Sets".

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Perhaps you are looking for something slightly different, but Cantor's "Contributions to the Founding of the Theory of Transfinite Numbers" is a delight to read.

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I believe, that it's "delight to read", but (as You already wrote) I'm looking for something different ;) –  exTyn Jan 2 '11 at 2:48
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Goldrei's Classic Set Theory is extremely well written and easy to read, and covers cardinalities

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There is Set Theory, by K. Kuratowski and A. Mostowski. It's dry as dirt and yet for some reason I loved reading that book.

If it's available in your library, I'd take it home and see if it works out.

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