Date: Feb 12, 2013 4:47 PM
Author: Virgil
Subject: Re: Matheology � 222 Back to the roots

In article 
WM <> wrote:

> On 12 Feb., 18:13, William Hughes <> wrote:
> > On Feb 12, 2:12 pm, WM <> wrote:
> >

> > > There is no line of the list that contains all FISs of d (because
> > > there are not all).

> >
> > Your claim is that there is a line of the list that contains
> > every FIS of d (there is no mention of all)

> But you seem to interpret some completeness into "every".
> Remember, beyond *every* FIS there are infinitely many FISs.

But no FISs beyond *every* FIS.
> >
> > you also claim
> >
> > the potentially infinite sequence d is not equal to the
> > potentially infinite sequence given by a line of the list.

> The lines of the list are finite.
> 1
> 12
> 123
> ...
> Or does that property disturb you?I use this model only because it is
> simpler to treat.

> >
> > Note that a potentially infinite sequence x is
> > equal to a potentially infinite sequence y iff
> > every FIS of x is a FIS of y and every FIS of
> > y is a FIS of x.  No mention or need of completion.

That does not hold when comparing an infinite sequences of finite
sequences of digits with an infinite sequence of digits.

A FIS of a sequence of sequences is not the same as a FIS of a sequence
of individuals. at least not for sequences of more than one object.

For WM's argument to be calid here one would have to have sequences of 2
or more digits identical to single digits.

You must also ASSUME the existence of your allegedly potentially
infinite sets which behave as you claim.
But unlike such set theories as ZF or NBG, you do not have an axiom
system that can be tested for consistency, so there is no way to test
your claims.
> Just that is obviously realized in above list. Every FIS of d is a
> line and every FIS of a line is a FIS of d.

l1 = 0
l2 = 10
l3 = 110
and so on with line ln = being n-1 "1"'s followed by "0".

And let d = 111... with no 0 in it ever.

Then no FIS of d is any line
and at least one FIS of any line is NOT a FIS of d.