Virgil
Posts:
4,479
Registered:
1/6/11
|
|
Re: Matheology � 201
Posted:
Jan 27, 2013 5:46 PM
|
|
In article
<b7014dbc-fcf0-4c1e-8f2a-e29dfda4c183@u20g2000yqo.googlegroups.com>,
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.
--
|
|
