🚀 go-pugleaf

On Mar 21, 11:06 am, Graham Cooper <grahamcoop...@gmail.com> wrote:
> On Mar 21, 10:41 pm, William Hughes <wpihug...@gmail.com> wrote:
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> > On Mar 21, 9:11 am, Graham Cooper <grahamcoop...@gmail.com> wrote:
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> > > On Mar 21, 9:30 pm, William Hughes <wpihug...@gmail.com> wrote:
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> > > > On Mar 21, 8:19 am, Graham Cooper <grahamcoop...@gmail.com> wrote:
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> > > > > On Mar 21, 9:09 pm, William Hughes <wpihug...@gmail.com> wrote:
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> > > > > > On Mar 21, 4:09 am, Graham Cooper <grahamcoop...@gmail.com> wrote:
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> > > > > > > On Mar 21, 4:54 pm, William Hughes <wpihug...@gmail.com> wrote:
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> > > > > > > > On Mar 21, 3:33 am, Graham Cooper <grahamcoop...@gmail.com> wrote:
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> > > > > > > > > On Mar 21, 2:30 pm, William Hughes <wpihug...@gmail.com> wrote:
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> > > > > > > > > > > My point is you can't support your claim with 2 given diagonals.
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> > > > > > > > > > My claim is that given a list of binary sequences I can find a
> > > > > > > > > > sequence
> > > > > > > > > > not on the list.
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> > > > > > > > > > To support this claim I need only one diagonal.  When you gave me
> > > > > > > > > > two diagonals I chose one and supported the claim.
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> > > > > > > > > > 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
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> > > > > > > > > You haven't proven your sequence is not on the list in the 2 diagonal
> > > > > > > > > version.
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> > > > > > > > > AD1 = 1110...
> > > > > > > > > AD2 = 0110...
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> > > > > > > > > Can you prove EITHER real is missing from my (secret) list given only
> > > > > > > > > the above?
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> > > > > > > > > IF YES, then by all means do so!
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> > > > > > > > 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-
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> > > > > > > Well that was concise!
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> > > > > > > But it's invalid due to the pigeon hole principle.
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> > > > > > > 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.
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> > > > > > The pigeon hole principle does not work
> > > > > > for infinite sets.
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> > > > > >                  - William Hughes-
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> > > > > I'm not slotting infinite sequences into infinite pigeon holes.
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> > > > Correct.  As usual you are arguing about infinite sets
> > > > using concepts that only work for finite sets.
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> > > > Recall
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> > > >  The anti-diagonal is formed by taking the
> > > >  diagonal and changing every 0 to 1 and 1 to 0.
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> > > > 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.
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> > > >                          - William Hughes-
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> > <snip discussion based on properties of finite sets>
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> > Please discuss directly why you cannot take the diagonal
> > and change ever 0 to 1 and every 1 to 0.
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> >                            - William Hughes
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> > PS.  An example of a list an an anti-diagonal
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> > List formed by counting in binary (n'th row is binary
> > expression for n followed by an infinite string of 0's.
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> > 0000...
> > 1000...
> > 10000...
> > 11000...
> > ...
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> > Anti-diagonal is an infinite string of 1's
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> Because it's a naive definition of a sequence that sometimes directly
> contradicts the definition of diagonal.

This contradiction can only happen with a list
containing every real number.

For L1 not containing every real number I can certainly
form the sequence

L(1,1), L(2,2), L(3,3) ...

and change every 0 to 1 and every 1 to 0.

Your claim is that the is a list L2 for which
I cannot do this.

                       - William Hughes