Date: Feb 5, 2013 11:03 AM
Subject: Re: Matheology § 203
On 5 Feb., 15:11, William Hughes <wpihug...@gmail.com> wrote:
> > > More importantly, we have learned that
> > > we can use induction to show "every"
> > > and that "every n -> P(n)" is equivalent
> > > to "there is no m such that ~P(m)"
> > > So we do not need to resort to "all"
> > > to show something does not exist.
We have learned that one of the applications of this lemma (in fact
the most important one) is the list itself that contains up to every
line n only lines from 1 to n, therefore it contains no line m such
that the potentially infinite sequence of lines 1, 2, 3, ... is
contained up to line m.