Re: Cantor's diagonal proof wrong?

From: Curt Welch (curt_at_kcwc.com)
Date: 11/22/04 

Date: 22 Nov 2004 01:07:16 GMT

David C. Ullrich <ullrich@math.okstate.edu> wrote:
> On 21 Nov 2004 00:10:09 GMT, curt@kcwc.com (Curt Welch) wrote:
>
> >stephen@nomail.com wrote:
> >> Curt Welch <curt@kcwc.com> wrote:
> >> : But, I can specify one special mapping function that works like
> >> : this. Fill the first row with any combination of 1's and 0's you
> >> : like. Then, fill every following row, with a copy of the row above
> >> : it, with the diagonal digit inverted.
> >>
> >> So your list possibly looks like
> >>
> >> 0000000000000000000000000000....
> >> 0100000000000000000000000000....
> >> 0110000000000000000000000000....
> >> 0111000000000000000000000000....
> >> 0111100000000000000000000000....
> >> ...............
> >>
> >> : Now, what I can show about your diagonal value, is that every
> >> : diagonal you construct is in fact in the table, in row N+1.
> >>
> >> No, it is not. I am only going to construct a single diagonal value,
> >> which will be
> >> 10000000000..........
> >> which is obviously nowhere in your list.
> >>
> >> Once again you have shown you do not understand what you are talking
> >> about.
> >
> >I shake my head in disbelief that you would actually write that.
>
> Fine. But you're ignoring the simple _proof_ he gave that what you
> say happens simply doesn't happen. (Which just by coincidence is
> exactly the same as the explanation I just gave before seeing
> his post.)

Yeah, it's hard to keep up with all the posts and not get behind in the
comments. It's kinda like trying to have a conversation with 10 people at
once. :)

The point of my "shake my head comment", is that his counter argument
missed the point of what I was trying to show. I was arguing apples and he
started to talk about oranges.

I was NOT trying to show a one to one mapping of the natrual numbers to the
reals, or that there was a one to one mapping from the natural numbers to
all strings of 1s and 0s. I was only trying to demonstrate how (in my
universe where everything is a procedure) that the diagonal argument is not
a valid proof - that it proves nothing one way or the other about the
mapping.

And both of you misunderstood what table I was talking about - but I'll
clear that up in another post in a minute. 

-- 
Curt Welch                                            http://CurtWelch.Com/
curt@kcwc.com                                        http://NewsReader.Com/

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