Virgil
Posts:
4,479
Registered:
1/6/11
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Re: WMatheology � 191
Posted:
Jan 16, 2013 2:44 AM
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In article
<0d0383dd-82ff-420c-a045-461df2411abd@u19g2000yqj.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 15 Jan., 22:56, Virgil <vir...@ligriv.com> wrote:
>
> > Why can my string not differ from the nth finite string in your listing
> > of finite strings in that string's nth place, if that string has one,
> > and by having anything in my strng's nth place if your nth string is not
> > n places long?
> > I see no reason why my string cannot differ from each string in your
> > whole list of strings according to such a rule.
>
> Your string can and will differ from the nth string. But there will
> always an identical string be in the list
Identical to what? no finite string can ever be identical to the
infinite string, and having any finite string repeated does not support
WM's claimed but false result.
> by construction. Every
> finite string means that there is no chance to construct something
> deviating from all.
That only hold in WMytheology, if anywhere.
Outside of WMytheology, the Cantor diagonal argument works equally well
on lists of finite sequences.
Note that any finite sequences on a set of n symbols matches an infinite
sequence on n+1 symbols by filling in all infinitely many unfilled
spaces in each sequnce with the extra symbol.
Thus WM's infinite list of finite sequences argument is just special
case of Cantor's infinite list of infinite sequences arguments, and thus
fails.
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