Re: Zenkin's paper on Cantor
From: Ross A. Finlayson (raf_at_tiki-lounge.com)
Date: 10/02/04
- Next message: Gregory L. Hansen: "Re: J. Advanced SR-cult Idiocies and Corruption"
- Previous message: Jack Sarfatti: "Brian Greene's Higgs Ocean and its implications for Haisch, Puthoff, Rueda ZPE inertia model"
- In reply to: No Way: "Re: Zenkin's paper on Cantor"
- Next in thread: Russell Easterly: "Re: Zenkin's paper on Cantor"
- Messages sorted by: [ date ] [ thread ]
Date: 1 Oct 2004 17:38:23 -0700
No Way <Not@real.com> wrote in message news:<h1hql010g9b6qac9fiqhdr8pjvrjamhho4@4ax.com>...
> On 29 Sep 2004 11:47:14 -0700, raf@tiki-lounge.com (Ross A. Finlayson)
> wrote:
>
> <snip>
>
> >You might claim that Cantor's first proof does not allow the mapping
> >of the integers to reals if the mapping would lead to a contradiction.
> > You construct an interval based upon alternately raising the lower
> >bound and lowering the upper bound according to his method, and find
> >that the first two element of the range are zero and iota. Iota is
> >defined to be the least positive real, and the "next" element after
> >zero on the real number line. Thus you are left with no
> >contradiction.
>
> Iota does not exist in the reals. There is no least positive real.
> Suppose there is a real A that is the least positive real. That would
> mean that (A/2) would also be positive real. (A/2)<A, so A can't be
> the least positive real. This argument applies to all possible choices
> for A (with A being a positive real).
>
> <snip>
My, what a pleasant meaningless notion that is obvious to everyone you
have discovered.
So... don't use iota as a convenient mental description of the least
positive real.
Particularly, not the one that sums over a natural scalar infinity to
one, and looks just like dx or perhaps dx.
Then, when you don't, there is still no entailing contradiction from
Cantor's first proof of the inability of mapping sets dense in the
reals such as the real numbers from the natural numbers. Use
epsilon-delta and be happy that each element of the range in order is
less than the next.
The concept of iota ia a convenient one.
Blank regards,
Ross F.
- Next message: Gregory L. Hansen: "Re: J. Advanced SR-cult Idiocies and Corruption"
- Previous message: Jack Sarfatti: "Brian Greene's Higgs Ocean and its implications for Haisch, Puthoff, Rueda ZPE inertia model"
- In reply to: No Way: "Re: Zenkin's paper on Cantor"
- Next in thread: Russell Easterly: "Re: Zenkin's paper on Cantor"
- Messages sorted by: [ date ] [ thread ]
Relevant Pages
|
