🚀 go-pugleaf

On Mar 21, 11:51 am, William Hughes <wpihug...@gmail.com> wrote:
> On Mar 20, 10:48 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
>
>
>
>
>
> > On Mar 21, 11:36 am, William Hughes <wpihug...@gmail.com> wrote:
>
> > > On Mar 20, 10:26 pm, William Hughes <wpihug...@gmail.com> wrote:
>
> > > > On Mar 20, 11:32 am, Graham Cooper <grahamcoop...@gmail.com> wrote:
>
> > > > > On Mar 20, 8:51 am, William Hughes <wpihug...@gmail.com> wrote:
>
> > > > > > Can you give a specific example of a set theory in which
> > > > > > there is no example of
>
> > > > > >   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.
>
> > > > > > ?
>
> > > > > Yep!  ZFC in fact!
>
> > > > > LIST1
> > > > > [0]001....
> > > > > 1[0]01....
> > > > > 00[0]1....
> > > > > 111[1]....
> > > > > ...
>
> > > > > DIAG1 = 0.0001...
>
> > > > > LIST2 = LIST1.ROWSWAP(1,2)
>
> > > > > [1]001....   = LIST1(Row2)
> > > > > 0[0]01....   = LIST1(Row1)
> > > > > 00[0]1....
> > > > > 111[1]....
> > > > > ...
>
> > > > > DIAG2 = 0.1001...
>
> > > > > I can submit either of DIAG1 or DIAG2 for the anti-diag proof.
>
> > > > > DIAG1 = 0.0001...
> > > > > DIAG2 = 0.1001...
>
> > > > > The digit expansions after digit 1 are identical.
>
> > > > 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
>
> > > Well that was piffle  (I was thinking of something else).  The
> > > diagonals
> > > can clearly be the same.
>
> > > One real that is missing from the list is
>
> > > 0.1110...
>
> > >                    - William Hughes-
>
> > And another missing real, without looking too hard?
>
> 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.
>

YOU WON'T LOOK AT ALL?

BUT IT'S RIGHT THERE!

There is an explictly obvious second missing real that follows.

I GIVE YOU
DIAG1 = 0.0001...
DIAG2 = 0.1001...

where the digit expansions after digit 1 are identical.

YOU GAVE
AD1 = 0.1110...

Why do you refuse to add
AD2 = 0.0110...

After all, you claim that any digit of the diagonal is arbitrary and
that does not affect your proof.


SO LET'S GO OVER THE STATUS QUO OF HIGHER INFINITY TO DATE.
(something that is 100 years overdue!)


NOBODY NEEDS TO LOOK AT ALL AT A CONCRETE EXERCISE TO DEMONSTRATE
CANTOR'S PROOF!

All of sci.math are like kids with alphabet blocks building an arch,
telling construction engineers they DON'T EVEN NEED TO LOOK AT THE
GOLDEN GATE BRIDGE because their bridge works!