Hi,

I'm looking for 3 or 4 good books on the topic of infinity, ideally aimed at an undergraduate or graduate mathematician and concerned with the "maths" rather than "physics" of infinity. Also I'd quite like a chapter or two to be devoted to Cantor and the continuum hypothesis. Can anyone recommend any? I've tried amazon without too much success; most popular science / maths books are understandably lacking on the technical side.

Thanks!

You will find what you seek at Universities.

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"Understanding Infinity: The Mathematics of Infinite Processes", By Gardiner

Though I don't think there is really any on the Continuum-Hypothesis, as the focus is more towards analysis.

Thanks. The book by Gardiner is a good suggestion but I'm really after something which has a focus strictly on infinity (in the way a layman would think of the topic, rather than as a motivation for calculus, but written at a fairly advanced level). There well may not be such a book, but I thought I'd ask.

Most of the other books on infinity that I have come across are written more for laymen, but lack any degree of mathematical rigor.

It is throught the eyes of set theory, I believe, that we discover the more beautiful (aka, weirder) parts of infinity. For instance, the continuum hypothesis looks at whether there are sets of cardinality (size) between that of the real numbers and that of the natural numbers. Thus, I would first recommend a book on relatively elementary set theory, although this book need not be big, and only then a book on the infinite (assuming, of course, your knowledge of sets isn't great).

As to what books to recommend, I'm afraid I cannot help you as I haven't read any books in this area specifically, although I believe "Elements of Set Theory" by Enderton is relatively standard. There is also an interesting looking book called "Set Theory and the Continuum Hypothesis", which sounds promising, and it is by Paul Cohen, which means it is promising (it was his and Godel's proofs that showed that the CH could never be proved nor disproved using ZF(C?)).

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