Re: Cantor and the binary tree



Virgil wrote:

> >
> > Every countable set like N is potentially infinite but not actually
> > infinite
>
>
> Then WM is only potentially numerate but not actually numerate.

Look here: The natural number n e N is nothing else than an
abbreviation of its initial segment {1,2,3,...,n} c N.
N consists exclusively of elements n. Similarly N consists exclusively
of subsets = initial segments (all of which include 1). There is no
element of N which is not an element of such a subset. And there is not
a pair of different elements n and n' of N, which satisfy the following
condition:
n belongs to an initial segment S which does not contain n'
and
n' belongs to an initial segment S' which does not contain n
in short:
n e S and n' !e S and n' e S' and n !e S'.
As this requirement is impossible to satisfy, the segment of n includes
all elements less than n. This holds for any n e N. Therefore N is a
segment. This segment is potentially infinite, because there is no
largest n and because it can be mapped on a proper subset.
Nevertheless, it is not actually infinite.

> WM's problem is that a set that is only potential is not a set at all.
> Sets must be well defined. Whatever it is that WM is describing is not a
> well defined set.

There are no well defined sets other than finite sets.

Regards, WM

.

Relevant Pages

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