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

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

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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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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

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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