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

 Messages: [ Previous | Next ]
 William Hughes Posts: 2,330 Registered: 12/7/10
Re: Matheology § 201
Posted: Jan 28, 2013 3:58 AM

On Jan 28, 9:45 am, WM <mueck...@rz.fh-augsburg.de> wrote:
> On 28 Jan., 08:44, William Hughes <wpihug...@gmail.com> wrote:
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> > On Jan 27, 11:23 pm, William Hughes <wpihug...@gmail.com> wrote:
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> > > On Jan 27, 11:16 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> > > > On 27 Jan., 23:02, William Hughes <wpihug...@gmail.com> wrote:
>
> > > > > On Jan 27, 10:39 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
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> > > > > > On 27 Jan., 21:40, William Hughes <wpihug...@gmail.com> wrote:
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> > > > > > > On Jan 27, 6:46 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
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> > > > > > > > On 27 Jan., 18:32, William Hughes <wpihug...@gmail.com> wrote:
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> > > > > > > > > On Jan 27, 6:05 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
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> > > > > > > > > <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.

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> > > > > > > > No.
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> > > > > > > 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.

>
> I did not agree to that,
>
>
>

> > 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.-

>
> You have not yet understood.

Either

i and ii. cannot be true at the same time.
i. true implies ii. false

or

It is not know that i. and ii. cannot be
true at the same time

i. true does not imply ii. false

Are you claiming that it is not known that i.
and ii. cannot be true at the same time?