Date: Feb 11, 2013 4:40 PM
Author: Virgil
Subject: Re: Matheology � 222 Back to the roots

In article 
<9f0b86ba-50b9-4692-8858-6b0788c7ed0c@x15g2000vbj.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:

> 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?


Every member of a sequence can be in a list of members of sequences
without the sequence being in the list of sequences.

Consider the list
L1 = 1, L2 = 2, L3 = 3
Which does not contain D = 123
even though every member of D is in one of L1 or L2 or L3

WM's claim is no more true than claiming that the union of a family of
sets must be one of the family being unioned.

The union of all FISONs (finite initial segments of naturals) is not a
FISON.

Given a list of all FISONs, the union of them is not a FISON.
Thus give a list of successively FISON-long strings, a string as long as
their union cannot be one of them.
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