On Sun, 28 Oct 2012 19:20:51 -0700 (PDT), Arturo Magidin <email@example.com> wrote:
>> How can this be unclear? > >Because I did not simply state the conclusion. >I gave you the "diagonal argument".
I did not recognize the argument you gave as a/the "diagonal" argument. I saw a separate argument for the same conclusion.
The diagonal argument as I've seen it starts with enumerations of numbers, selects out digits, and constructs from those digits, and then makes an assertion about the result.
>If you are questioning whether it is "coherent", then you should >point to whatever point you find incoherent, rather than simply >quote and then give a sentence fragment.
This is (perhaps too obviously) not my area of expertise, and rather than try to present my own proof or even formal objection at this point - I came looking for further background.
>The government doesn't like it when I read minds without a >warrant, so I try not to do it, you see.
There are constructivist objections to the whole enterprise. If nothing else, I was hoping to see something like these addressed against the diagonal argument piecemeal. I'm not really versed in constructivist mathematics as such either, and really, the only point of contact that I have curiosity about at this point is trying to compare and contrast on this diagonal argument.
I'm vaguely aware of some of the several paradoxes of set theory. Another question I have is whether the structure of the diagonal argument doesn't include something like that. People seem happy to live with these paradoxes, if there's one more I don't suppose that upsets the apple cart, but I might find it - interesting.
>I have given you a complete proof of Cantor's Theorem; the >diagonal argument is embedded in that theorem.
What does that mean to you, or me: "embedded"?
Can you throw me a bone here, like use the word "diagonal"?
>What is it that you find incoherent?
Is it not true that what you've given is more like a rephrased version of Cantor's original proof, and not at all of his later offered diagonal argument?