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Topic: Matheology § 201
Replies: 32   Last Post: Jan 28, 2013 2:26 PM

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 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
Re: Matheology § 201
Posted: Jan 27, 2013 5:16 PM
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On 27 Jan., 23:02, William Hughes <wpihug...@gmail.com> wrote:
> On Jan 27, 10:39 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
>
>
>
>

> > On 27 Jan., 21:40, William Hughes <wpihug...@gmail.com> wrote:
>
> > > On Jan 27, 6:46 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> > > > On 27 Jan., 18:32, William Hughes <wpihug...@gmail.com> wrote:
>
> > > > > On Jan 27, 6:05 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> > > > > <snip>
>
> > > > > >..the diagonal
> > > > > > cannot differ from all lines
> > > > > > (it differs from every line, though).

>
> > > > > The fact that the diagonal differs from every line is
> > > > > enough to show (induction) that the diagonal is not
> > > > > equal to any line in the list.

>
> > > > No.
>
> > > Let the antidiagonal be d and the nth line be l(n)
>
> > > We know that for each n in |N, d is not equal to l(n)
>
> > > You have agreed that this implies
>
> > > There is no m in |N such that d equals l(m)
>
> > No.
>
> You contradict yourself.  You have agreed
> that if P(n) is true for every n then
> the is no n such that P(n) is false.

Don't turn the words in my mouth. I have agreed that if P(n) is true
for every n, then it cannot be concluded that it is true for all n.

Example:
For every n, there are infinitely many m > n.
For all n, this is not true.

Regards, WM

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