Date: May 7, 2013 9:50 PM
Author: Graham Cooper
Subject: Re: The Uncountability of the Real Numbers in the Calculus.

On May 8, 11:04 am, Zeit Geist <tucsond...@me.com> wrote:
> > 0.3..  is missing!!
>
> > WOW!   The IGNORE_ALL_QUALITATIVE_STRING_COMPARISONS TRICK!
>
> > Herc
>
> > --
>
> The answer is missing.
>
> WOW! The ignore the question trick.
>
> ZG
>


I did give an example.


"The completeness of the real numbers implies that
any strictly increasing sequence of countable length

A
A + bit more
A + bit more + bit more
(AND SO ON)


has a least upper bound that is a real number but not a
member of the sequence."


A + bit more + bit more + ... FOR EVER
=/=
A
or
A + bit more
or
A + bit more + bit more
or
...



--------------

I'm not up to Infinite Sequences of Infinite Sequences in PROLOG yet

since:

subset( S1 , S2 ) :- e( @A , S1 ) , e( A , S2 )

by extension only works on finite sets.

What's needed is a systematic test for equivalent infinite sequences
by Induction.

Without Induction, all your infinite sums over MODULO arithmetic
operators are ill defined.

--------------


Herc
--

CANTORS POWERSET PROOF

| CARDINALITY | > | INFINITY |

IF SET1 has 1 - then MYSET skips 1
or
IF SET1 skips 1 - then MYSET has 1

AND
IF SET2 has 2 - then MYSET skips 2
or
IF SET2 skips 2 - then MYSET has 2

AND
IF SET3 has 3 - then MYSET skips 3
or
IF SET3 skips 3 - then MYSET has 3

AND
IF SET4 has 4 - then MYSET skips 4
or
IF SET4 skips 4 - then MYSET has 4
...