Date: Feb 14, 2013 2:26 AM
Subject: Re: Matheology § 222 Back to the roots
On 13 Feb., 23:22, William Hughes <wpihug...@gmail.com> wrote:
> On Feb 13, 9:03 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> > You cannot discern that two potentially infinity sequences are equal.
> > When will you understand that such a result requires completeness?
> Two potentially infinite sequences x and y are
> equal iff for every natural number n, the
> nth FIS of x is equal to the nth FIS of y
And just this criterion is satisfied for the system
For every n all FISs of d are identical with all FISs of line n.
> No concept of completeness is needed or used.
That means we have to go to n only.
> we can use induction to show
> is equal to
And the three points stand for every finite number, but not for all.
> Consider the list of potentially infinite sequence
> The diagonals are both
And again you confuse every with all.
> It makes perfect sense to say that there
> is no line in L1 that is equal
> to d
Do you claim that the list
does not contain every FIS of d?
Do you claim that there are two or more FISs of d that require more
than one line for their accomodation?
We can use induction to show that!
Ponder about this question and then try to make perfect sense.