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

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: Matheology � 201
Posted: Jan 27, 2013 5:46 PM

In article
WM <mueckenh@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. 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.

For all n in |N it is true:
For all n, n in |N => exist infinitely many m in |N with m > n.
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