Date: Feb 7, 2013 4:50 AM
Author: William Hughes
Subject: Re: Matheology § 222 Back to the roots

On Feb 7, 10:18 am, WM <mueck...@rz.fh-augsburg.de> wrote:
> On 7 Feb., 10:11, William Hughes <wpihug...@gmail.com> wrote:
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> > On Feb 7, 10:05 am, WM <mueck...@rz.fh-augsburg.de> wrote:
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> > > On 7 Feb., 10:03, William Hughes <wpihug...@gmail.com> wrote:
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> > > > On Feb 7, 7:45 am, WM <mueck...@rz.fh-augsburg.de> wrote:
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> > > > > Matheology § 222   Back to the roots
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> > > > > Consider a Cantor-list with entries a_n and anti-diagonal d:
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> > > > Then, according to WM, d is not a line of the list.
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> > > Do you agree that the logic applied in set theory does not make a
> > > difference between "for every" and "for all"?
> > > Can you explain why here, in this decisive case, a difference appears
> > > nevertheless?

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> > Since neither standard set theory, nor the concept "all" is used
> > by WM in obtaining "d is not a line of the list"
> > I don't know what you mean by "a difference appears".

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> Look at the original post. Standard set theory is applied.


WM uses induction to show that for every natural
number n, d is not the nth line of the list.
He then uses the fact that this is equivalent to
"there does not exist an m, such that d is the mth
line of the list". At no time does he assume that
"all" lines exist.