Re: Cantor's diagonal proof wrong?

From: facedancer (facedancer7_at_yahoo.com)
Date: 11/18/04 

Date: Thu, 18 Nov 2004 17:17:37 +0000 (UTC)

On 15 Nov 2004, Curt Welch wrote:
>"robert j. kolker" <nowhere@nowhere.net> wrote:
>> Curt Welch wrote:
>>
>> > But now I'm starting to wonder if there may be value in looking at this
>> > differently. Might it be valid to think of division of 1 by 9 as an
>> > infinite processes (algorithm) that produces closer and closer
>> > approximations, yet is always unable to produce the actual "point" on
>> > the line?
>>
>> Nonesense. One can always divide a line segment into N equal parts by a
>> well known geometric construction. So getting the point on the segment
>> corresponding to k/N for k = 0,1,...N is trivial. Or equivalently choose
>> a unit length and lay out multiples of this length on an infinite ray.
>> Again one easily constructs points corresponding to k*N. Why do you
>> complicate a very straightforward matter?
>
>Because most things in life that seem straightforward turn out later to be
>anything but that. I enjoy finding the exceptions, so I search. But like
>fishing, many times, there is just nothing to be caught.
>
>--
>Curt Welch http://CurtWelch.Com/
>curt@kcwc.com http://NewsReader.Com/

Would you argue that 1/5 is also defined by an algorithm?
Probably not, because 1/5 = 0.2, a "nice" number. But why should the method of obtaining 1/5 differ from 1/9? It shouldn't. This occurs because of your choice of the decimal system. If you were to choose the system of 9 digits, then 1/9 would be a "nice 0.1" . Nut then 1/5, in this system, wouldn't be so "nice" anymore. Certainly, a theory about infinity, cannot depend on how many digits or symbols you use in your system.

facedancer

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