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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: 15,224
Registered: 1/29/05
Re: Matheology § 201
Posted: Jan 28, 2013 3:45 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On 28 Jan., 08:44, William Hughes <wpihug...@gmail.com> wrote:
> 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:
>
> > > 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.


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. For every natural n, P(n) is true does
not imply anything about the existence of P(m). You have not yet
grasped that there is no "for all".

Of course for every n it is true that there are infinitely many
naturals beyond.
Of course there is no m such that there is no natural beyond.
But if you assume that all natural exist, then there is no natural
beyond all.

You must unederstand that, therefore, there is no "all naturals". All
we can do is state P(n) for every n. Nevertheless it is not
necessarily true for all n.

Regards, WM


Date Subject Author
1/27/13
Read Matheology § 201
mueckenh@rz.fh-augsburg.de
1/27/13
Read Re: Matheology § 201
William Hughes
1/27/13
Read Re: Matheology § 201
mueckenh@rz.fh-augsburg.de
1/27/13
Read Re: Matheology § 201
William Hughes
1/27/13
Read Re: Matheology S 201
Jesse F. Hughes
1/27/13
Read Re: Matheology S 201
mueckenh@rz.fh-augsburg.de
1/27/13
Read Re: Matheology S 201
Jesse F. Hughes
1/27/13
Read Re: Matheology S 201
Virgil
1/27/13
Read Re: Matheology S 201
William Hughes
1/27/13
Read Re: Matheology § 201
mueckenh@rz.fh-augsburg.de
1/27/13
Read Re: Matheology § 201
William Hughes
1/27/13
Read Re: Matheology § 201
mueckenh@rz.fh-augsburg.de
1/27/13
Read Re: Matheology � 201
Virgil
1/27/13
Read Re: Matheology § 201
William Hughes
1/27/13
Read Re: Matheology § 201
mueckenh@rz.fh-augsburg.de
1/27/13
Read Re: Matheology § 201
William Hughes
1/27/13
Read Re: Matheology § 201
mueckenh@rz.fh-augsburg.de
1/27/13
Read Re: Matheology § 201
William Hughes
1/28/13
Read Re: Matheology § 201
William Hughes
1/28/13
Read Re: Matheology § 201
mueckenh@rz.fh-augsburg.de
1/28/13
Read Re: Matheology § 201
William Hughes
1/28/13
Read Re: Matheology § 201
mueckenh@rz.fh-augsburg.de
1/28/13
Read Re: Matheology § 201
William Hughes
1/28/13
Read Re: Matheology § 201
mueckenh@rz.fh-augsburg.de
1/28/13
Read Re: Matheology § 201
William Hughes
1/28/13
Read Re: Matheology � 201
Virgil
1/28/13
Read Re: Matheology � 201
Virgil
1/28/13
Read Re: Matheology � 201
Virgil
1/27/13
Read Re: Matheology � 201
Virgil
1/27/13
Read Re: Matheology � 201
Virgil
1/27/13
Read Re: Matheology � 201
Virgil
1/27/13
Read Re: Matheology � 201
Virgil
1/27/13
Read Re: Matheology � 201
Virgil

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