---> A FLAW IN CANTOR'S PROOF <---

Graham Cooper

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Sep 22, 2011, 4:28:52 AM9/22/11

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ANTID=ALL[d]:[ANTID[d]=/=LIST[d,d]] -> ALL[d]:[ANTID=/=LIST(d)]

in Maths courses they might call that "BIGGER than INFINITY"
but in Computer Science we call it "CURRYING a FUNCTION"!

Demonstration of a flaw in Cantor's proof.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Using an ANTIDIGIT function
digit = (digit + 1) mod 3

[1] CALCULATE A PUTATIVE INFINITE LIST OF REALS

---> HERE IS MY DECK OF CARDS!

1 0.2011212000
2 0.0002010201
3 0.1001211220
4 0.2021121120
5 0.1011000102
6 0.2021202020
7 0.0101100111
8 0.2101100020
9 0.0212111111
10 0.2022222200

.

[2] REMOVE SOME ROW - SAY ROW 3

---> PICK A CARD, ANY CARD, AND REMOVE IT FROM THE DECK!

1 0.2011212000
2 0.0002010201
4 0.2021121120
5 0.1011000102
6 0.2021202020
7 0.0101100111
8 0.2101100020
9 0.0212111111
10 0.2022222200
11 0.2002021100

.

--> NOW SHOW ME YOUR CARD!

[3] MISSING ROW 3 = 1001211220

ANTI (MISS. ROW 3) = 2112022001

.

[4] SORT THE SMALLER LIST SO ANTI-ROW-3 IS THE NEW DIAGONAL
(row 3 is missing - so the new diagonal anti-3 should fit!)

---> NOW I WILL SHUFFLE THE DECK!

1 0. 2 011212000
7 0.0 1 01100111
5 0.10 1 1000102
2 0.000 2 010201
11 0.2002 0 21100
4 0.20211 2 1120
6 0.202120 2 020
8 0.2101100 0 20
10 0.20222222 0 0
9 0.021211111 1

SEE IF YOU CAN USE CANTORS PROOF TO FIND THE MISSING ROW!

DIAGONAL = 2112022001

ANTIDIAGONAL = 0220100112 #

BZZT! THAT ANTIDIAGONAL IS NOT THE OLD ROW 3!

TRY ANTIDIGIT function
digit = (digit-1) mod 3

ANTIDIAGONAL2 = 1001211220 = MISSING ROW 3

---> IS THIS YOUR CARD?

CANTOR'S DIAGONAL METHOD IS VERIFIED!
IT FOUND THE ROW THAT WE REMOVED FROM THE ORIGINAL LIST AS MISSING!

----

Does anyone see the flaw?
HINT: #

Herc

Prai Jei

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Sep 22, 2011, 2:25:52 PM9/22/11

to

Graham Cooper set the following eddies spiralling through the space-time
continuum:

> [1] CALCULATE A PUTATIVE INFINITE LIST OF REALS
>
> ---> HERE IS MY DECK OF CARDS!
>
> 1 0.2011212000
> 2 0.0002010201
> 3 0.1001211220
> 4 0.2021121120
> 5 0.1011000102
> 6 0.2021202020
> 7 0.0101100111
> 8 0.2101100020
> 9 0.0212111111
> 10 0.2022222200
>

> Does anyone see the flaw?
> HINT: #
>
> Herc

The putative infinite list is in fact *finite* - as any example presented
here or in any other scientific forum must be, for lack of paper / memory
capacity / quanta in the universe.

If the list of reals were truly infinite, any real would appear somewhere in
it, if not at a finite-numbered position then at an infinite-numbered
position.

There is only one Infinity, and Cantor is not Her prophet.
--
ξ:) Proud to be curly

Interchange the alphabetic letter groups to reply

SPQR

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Sep 22, 2011, 5:07:44 PM9/22/11

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In article <j5fujm$a4s$1...@dont-email.me>,

Prai Jei <pvstownse...@ntlworld.com> wrote:

> Graham Cooper set the following eddies spiralling through the space-time
> continuum:
>
> > [1] CALCULATE A PUTATIVE INFINITE LIST OF REALS
> >
> > ---> HERE IS MY DECK OF CARDS!
> >
> > 1 0.2011212000
> > 2 0.0002010201
> > 3 0.1001211220
> > 4 0.2021121120
> > 5 0.1011000102
> > 6 0.2021202020
> > 7 0.0101100111
> > 8 0.2101100020
> > 9 0.0212111111
> > 10 0.2022222200
> >
> > Does anyone see the flaw?
> > HINT: #
> >
> > Herc
>
> The putative infinite list is in fact *finite* - as any example presented
> here or in any other scientific forum must be, for lack of paper / memory
> capacity / quanta in the universe.
>
> If the list of reals were truly infinite, any real would appear somewhere in
> it, if not at a finite-numbered position then at an infinite-numbered
> position.

Excepts that lists, by definition, do not have any infinite-numbered
positions.

>
> There is only one Infinity, and Cantor is not Her prophet.

What makes you think infiniteness has a gender?

Prai Jei

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Sep 24, 2011, 2:40:45 PM9/24/11

to

SPQR set the following eddies spiralling through the space-time continuum:

>> If the list of reals were truly infinite, any real would appear somewhere
>> in it, if not at a finite-numbered position then at an infinite-numbered
>> position.
>
> Excepts that lists, by definition, do not have any infinite-numbered
> positions.

Not even infinite lists? Even the integers form an infinite set so any
complete list of them, placed in 1:1 correspondence with a purported
complete list of reals, must be of infinite length. After all, the whole
object of the exercise is to try to prove that some infinities are greater
than others, ĉu ne? Myself, I still don't see the joke.

>> There is only one Infinity, and Cantor is not Her prophet.
>
> What makes you think infiniteness has a gender?

Poetic licence.