```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:>>>>>>>>>> > On Feb 7, 10:05 am, WM <mueck...@rz.fh-augsburg.de> wrote:>> > > On 7 Feb., 10:03, William Hughes <wpihug...@gmail.com> wrote:>> > > > On Feb 7, 7:45 am, WM <mueck...@rz.fh-augsburg.de> wrote:>> > > > > Matheology § 222   Back to the roots>> > > > > Consider a Cantor-list with entries a_n and anti-diagonal d:>> > > > Then, according to WM, d is not a line of the list.>> > > 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?>> > 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".>> Look at the original post. Standard set theory is applied.WM uses induction to show that for every naturalnumber 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 mthline of the list".  At no time does he assume that"all" lines exist.
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