Date: Feb 11, 2013 2:20 PM
Subject: Re: Matheology § 222 Back to the roots
On 11 Feb., 19:57, William Hughes <wpihug...@gmail.com> wrote:
> L is a potentially infinite list.
> d, the diagonal is a potentially
> infinite sequence
and therefore is not complete.
> for every n, the nth line of L is
> a potentially infinite sequence.
We can say so. But for sake of simplicity consider the list
with indexed symbols o_jk
> We get from induction,
> for every natural number n,
> the potentially infinite sequence
> d is not equal to the potentially
> infinite sequence given by the nth line.
> We conclude, there does not exist a
> natural number m, such that
> the potentially infinite sequence d,
> is equal to the potentially infinite
> sequence given by the mth line.
> d is a potentially infinite sequence
> each line of the list is a potentially infinite sequence
> We show that there is no
We show that the potentially infinite diagonal is in the list by
proving that every o_nn is in the list. And every o that is in the
list, is in some line of the list. And everything that is in some line
of the list is in one line of the list.
Anything wrong with this conclusion?
Then give a counter-example.