🚀 go-pugleaf

On Mar 21, 12:53 am, Graham Cooper <grahamcoop...@gmail.com> wrote:
> On Mar 21, 1:21 pm, William Hughes <wpihug...@gmail.com> wrote:
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> > On Mar 20, 11:54 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
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> > > On Mar 21, 11:51 am, William Hughes <wpihug...@gmail.com> wrote:
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> > > > On Mar 20, 10:48 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
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> > > > > On Mar 21, 11:36 am, William Hughes <wpihug...@gmail.com> wrote:
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> > > > > > On Mar 20, 10:26 pm, William Hughes <wpihug...@gmail.com> wrote:
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> > > > > > > On Mar 20, 11:32 am, Graham Cooper <grahamcoop...@gmail.com> wrote:
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> > > > > > > > On Mar 20, 8:51 am, William Hughes <wpihug...@gmail.com> wrote:
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> > > > > > > > > Can you give a specific example of a set theory in which
> > > > > > > > > there is no example of
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> > > > > > > > >   There exists a collection E, such that given any list
> > > > > > > > >   L of members of E, there exists a member of E not on the list.
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> > > > > > > > > ?
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> > > > > > > > Yep!  ZFC in fact!
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> > > > > > > > LIST1
> > > > > > > > [0]001....
> > > > > > > > 1[0]01....
> > > > > > > > 00[0]1....
> > > > > > > > 111[1]....
> > > > > > > > ...
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> > > > > > > > DIAG1 = 0.0001...
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> > > > > > > > LIST2 = LIST1.ROWSWAP(1,2)
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> > > > > > > > [1]001....   = LIST1(Row2)
> > > > > > > > 0[0]01....   = LIST1(Row1)
> > > > > > > > 00[0]1....
> > > > > > > > 111[1]....
> > > > > > > > ...
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> > > > > > > > DIAG2 = 0.1001...
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> > > > > > > > I can submit either of DIAG1 or DIAG2 for the anti-diag proof.
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> > > > > > > > DIAG1 = 0.0001...
> > > > > > > > DIAG2 = 0.1001...
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> > > > > > > > The digit expansions after digit 1 are identical.
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> > > > > > > They can't be.  They can be identical for any finite stretch
> > > > > > > you like, however they cannot be identical for an infinite
> > > > > > > stretch.
> > > > > > >                         - William Hughes
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> > > > > > Well that was piffle  (I was thinking of something else).  The
> > > > > > diagonals
> > > > > > can clearly be the same.
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> > > > > > One real that is missing from the list is
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> > > > > > 0.1110...
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> > > > > >                    - William Hughes-
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> > > > > And another missing real, without looking too hard?
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> > > > There are lots and lots (indeed any random real will be
> > > > missing from the list with probability 1.) However, I only
> > > > need one so I wont look at all.
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> > > YOU WON'T LOOK AT ALL?
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> > No, I don't have to.  I have already noted that uncountably
> > others exist.  And I acknowledge that you can get some by
> > using "generalized" diagonals.  However, they are irrelevant
> > to the claim that one such number exists.
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> > If you have a point to make, make it,  You are as capable
> > of reversing DIAG2 as I am.
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> 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