|
|
Re: Matheology § 201
Posted:
Jan 27, 2013 5:02 PM
|
|
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.
(E.g. For every n, n has a prime decomposition
therefore there is no n that does not have
a prime decomposition)
|
|
