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

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 William Hughes Posts: 2,330 Registered: 12/7/10
Re: Matheology § 201
Posted: Jan 28, 2013 2:44 AM
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On Jan 27, 11:23 pm, William Hughes <wpihug...@gmail.com> wrote:
> On Jan 27, 11:16 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
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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.
>
> You have apparently forgotten the
> thread in which you agreed to this.

A simple proof.

The statements

i. for every natural number n, P(n) is true
ii. there exists a natural number m such that P(m)
is false

cannot both be true at the same time.
If you prove that i. is true then it follows
that ii. is false.

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