Re: Cantor and the binary tree

In article <1118049790.420079.124240@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:

> Daniel W. Johnson wrote:
> > <mueckenh@xxxxxxxxxxxxxxxxx> wrote:
> >
> > > There is no largest natural number. Nevertheless
> > > there are less than 10^100 natural numbers.
> >
> > It can be proven that any finite non-empty totally ordered set has a
> > largest element. The set of natural numbers is non-empty, and the usual
> > order is a total order. What does this mean for your claims that the
> > set is finite but has no largest element?
>
> Look what I have to say about existence of numbers.
> http://www.fh-augsburg.de/~mueckenh/Infinity/P2%20R4%20final.doc
> also as .doc or .mht avaiable.

I have read enough of WM's monograph to see that WM's definition of
'number' is not compatible with mathematical definitions of number, so
that what WM says holds at most only in areas governed by his own
definitions and need not hold for anyone else's definitions.

In standard analysis, all of the 'inaccessible' real numbers have to be
there for the real number system to have the properties that wwe want it
to have.
.

Relevant Pages

  • Re: Cantor and the binary tree
    ... Daniel W. Johnson wrote: ... > order is a total order. ... Regards, WM ...
    (sci.math)
  • Re: Cantor and the binary tree
    ... >> Daniel W. Johnson wrote: ... >>> order is a total order. ... >> Look what I have to say about existence of numbers. ... > 'number' is not compatible with mathematical definitions of number, ...
    (sci.math)
  • Re: Cantor and the binary tree
    ... order is a total order. ... Daniel W. Johnson ... Prev by Date: ...
    (sci.math)
  • Re: exp(sqrt(2))
    ... While this theorem is sufficient to demonstrate that if x is a nonzero ... >countable subset of the reals; this leaves the set of real x such that ... >Daniel W. Johnson ...
    (sci.math)
  • Re: .99999... still=/= 1
    ... panoptes@iquest.net (Daniel W. Johnson) writes: ... -- James S. Harris on the path of self-discovery ...
    (sci.math)
Loading