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My real analysis book uses the Cantor's diagonal argument to prove that the reals are not countable, however the book does not explain the argument.

I would like to understand the Cantor's diagonal argument deeper and applied to other proofs, does anyone have a good reference for this?

Thank you in advance

Beaba
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  • In general, this is a technique called a diagonal argument, which involves some sort of self-reference to show a contradiction. If you want to learn more about Cantor's proof, there are two common variants. $(1)$: A construction which shows that you can always find a real number not in a countable list of reals in some $n$-ary expansion, and $(2)$: a general argument that assumes a surjection $X \rightarrow \mathcal{P}(X)$, and derives a contradiction. – While I Am Jan 19 '21 at 15:33
  • One of the most instructive things I can think of is to look at (informed) replies to criticisms of the diagonal argument. For instance, see Refuting the Anti-Cantor Cranks and the Linked and Related questions listed to the right side when you get there. Also, the Related questions listed to the right side of your question. – Dave L. Renfro Jan 19 '21 at 15:49
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    You'd better say what your book is, because otherwise, you risk to get recommendations for the same book, from those who understood it. –  Jan 19 '21 at 16:24

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