Date: Feb 11, 2013 4:40 PM
Subject: Re: Matheology � 222 Back to the roots
WM <email@example.com> 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
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.