🚀 go-pugleaf

On Mar 21, 10:41 pm, William Hughes <wpihug...@gmail.com> wrote:
> On Mar 21, 9:11 am, Graham Cooper <grahamcoop...@gmail.com> wrote:
>
>
>
>
>
> > On Mar 21, 9:30 pm, William Hughes <wpihug...@gmail.com> wrote:
>
> > > On Mar 21, 8:19 am, Graham Cooper <grahamcoop...@gmail.com> wrote:
>
> > > > On Mar 21, 9:09 pm, William Hughes <wpihug...@gmail.com> wrote:
>
> > > > > On Mar 21, 4:09 am, Graham Cooper <grahamcoop...@gmail.com> wrote:
>
> > > > > > On Mar 21, 4:54 pm, William Hughes <wpihug...@gmail.com> wrote:
>
> > > > > > > On Mar 21, 3:33 am, Graham Cooper <grahamcoop...@gmail.com> wrote:
>
> > > > > > > > On Mar 21, 2:30 pm, William Hughes <wpihug...@gmail.com> wrote:
>
> > > > > > > > > > My point is you can't support your claim with 2 given diagonals.
>
> > > > > > > > > My claim is that given a list of binary sequences I can find a
> > > > > > > > > sequence
> > > > > > > > > not on the list.
>
> > > > > > > > > To support this claim I need only one diagonal.  When you gave me
> > > > > > > > > two diagonals I chose one and supported the claim.
>
> > > > > > > > > Your claim that you can get a generalized diagonal with any finite
> > > > > > > > > prefix is true, but irrelevant.  You cannot set the generalized
> > > > > > > > > diagonal to an arbitrary sequence.
> > > > > > > > >                                      - William Hughes
>
> > > > > > > > You haven't proven your sequence is not on the list in the 2 diagonal
> > > > > > > > version.
>
> > > > > > > > AD1 = 1110...
> > > > > > > > AD2 = 0110...
>
> > > > > > > > Can you prove EITHER real is missing from my (secret) list given only
> > > > > > > > the above?
>
> > > > > > > > IF YES, then by all means do so!
>
> > > > > > > There is a sequence not on your secret list that starts
> > > > > > > 1100.  Proof: the n'th digit means that sequence is not
> > > > > > > the n'th line of the list.  There may be other sequences that
> > > > > > > starts 1110 on your secret list.
> > > > > > >                                  -William Hughes-
>
> > > > > > Well that was concise!
>
> > > > > > But it's invalid due to the pigeon hole principle.
>
> > > > > > My similar claim to yours is: no matter what numbers I put into the
> > > > > > pigeon holes, there are always more empty pigeon holes than filled
> > > > > > pigeon holes.
>
> > > > > The pigeon hole principle does not work
> > > > > for infinite sets.
>
> > > > >                  - William Hughes-
>
> > > > I'm not slotting infinite sequences into infinite pigeon holes.
>
> > > Correct.  As usual you are arguing about infinite sets
> > > using concepts that only work for finite sets.
>
> > > Recall
>
> > >  The anti-diagonal is formed by taking the
> > >  diagonal and changing every 0 to 1 and 1 to 0.
>
> > > Any claim that the anti-diagonal does not exist is
> > > silly.  Any claim that the anti-diagonal is equal to
> > > a row of the list is silly.
>
> > >                          - William Hughes-
>
> <snip discussion based on properties of finite sets>
>
> Please discuss directly why you cannot take the diagonal
> and change ever 0 to 1 and every 1 to 0.
>
>                            - William Hughes
>
> PS.  An example of a list an an anti-diagonal
>
> List formed by counting in binary (n'th row is binary
> expression for n followed by an infinite string of 0's.
>
> 0000...
> 1000...
> 10000...
> 11000...
> ...
>
> Anti-diagonal is an infinite string of 1's


Because it's a naive definition of a sequence that sometimes directly
contradicts the definition of diagonal.

A diagonal is a construction, just like LIST(1,1) . LIST(1,2) .
LIST(2,3) . LIST(2,4) . ...
is a construction.

There are oo like constructions equally as valid as the diagonal, and
it's kindergarten maths that you can't make a diagonal-like#
construction that equals an anti-row.

# = LIST(a,1) . LIST(b,2) . LIST(c,3) ...

Trivial kindergarten maths Will.

You NEVER create a unique seq. like

12
34

14 -> 25

THAT NEVER HAPPENS

and you NEVER get to choose the diagonal, there are oo sequences I can
give you independant of the list.

The only clause to the independence of the generalised diagonal to an
infinite digit plane is anti-rows.

Cantor's proof is ALL OVER THE PLACE.

You have supporting 'proofs' that are nothing more than conjecture,
about a dozen of them.

BUT... the WHOLE sequence seems different
BUT... who cares if there's no finite unique sequence, finite = bad
keyword like saying 'cheat' in a Texas bar
BUT... irrationals don't occur on finite digit string lists so...
BUT... you can't give me an anti-row for the diagonal so....
BUT...

BUT NOTHING WILL.

None of your counter arguments DEDUCE ANYTHING.

Why do you think...

X--
-X-
--X

produces a unique sequence when the order of the list is not even
given!

There is no diagonal on inifinite lists.

Just like there is nowhere to put your first [p] on my diagonal set.


Digit 1 of diagonal


-1--2--3--4--5--6--7--8--9--0-
[P][P][P][P][P][P][P][P][P][P]


Try some MATHS Will, not a foregone conclusion WHERE IS THE ANT-
DIAGONAL?

There are INFINITY of them, it's 100% white noise.