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

...