Date: Mar 21, 2013 3:20 PM
Subject: Re: Matheology § 224
On 3/21/2013 8:29 AM, WM wrote:
> On 21 Mrz., 14:02, William Hughes <wpihug...@gmail.com> wrote:
>>> But you think that after all finite and unnecessary lines another one
>>> is lurking like a dragon?
>> Now I think that after any finite set of unnecessary lines has
>> been removed, there still remains an unnecessary line.-
> I know. That's what I wished to prove. In order to believe in the
> existence of actually infinite sets, it is necessary to have another
> element after all ordinary elements have been removed. The set is more
> than its elements, namely at least one element more. The actually
> infinite set of finite natural numbers remains after all finite
> numbers have been removed, since it contains an infinite number. But
> that is unmathematical.
That the set is different from its
elements is precisely why logical
construction by classes takes the
form of a class hierarchy.
This is why the rational numbers
used to construct Dedekind cuts are
not the same as the rational numbers
represented by Dedekind cuts.
Because you do not bother to understand
these things, you confuse yourself and
blame it on Cantor.
But, Cantor explained himself clearly
on these matters. Thus the fault lies
Does anyone have a crayon to play with?