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Topic: Nathan counts the powerset
Replies: 144   Last Post: Jan 26, 1999 9:26 AM

 Messages: [ Previous | Next ]
 Nathaniel Deeth Posts: 548 Registered: 12/4/04
Re: Nathan counts the powerset
Posted: Dec 30, 1998 5:29 PM

On Tue, 29 Dec 1998 00:36:21 GMT, "Bob Street"
<bob@belgrave.clara.net> wrote:

>
>Mike Deeth wrote in message <3686D986.745ADAB8@ashland.baysat.net>...

>>
>>
>>Arturo Magidin wrote:
>>

>>> In article <3684404B.86724757@ashland.baysat.net>,

>>> >
>>> >

>> (2/3)(1-(1/2)^(n+1)) (even)
>># (1/3)(1-(1/2)^n) (odd) Diagonal Cantor's
>>--------------------------------------------------------
>>0 .10
>>1 .01 .01 .10
>>2 .1010
>>3 .0101 01 10
>>4 .101010
>>5 .010101 01 10
>>6 .10101010
>>7 .01010101 01 10
>>8 .1010101010
>>9 .0101010101 01 10
>>. .
>>. .
>>. .10101010101010101010...101010
>>. .01010101010101010101...010101
>>

>
>
>Arturo's *patch* solves the REAL (no pun intended) problem which the
>argument has in binary - it's not easy to demonstrate that a diagonal can be
>constructed which doesn't 'end' 11111111111111............ in binary,
>because there aren't enough digits to play with. In any other base (10 for
>example) we can construct a diagonal using only the digits 3 and 4 (for
>example), thus we know that it doesn't end 999999999.............
>Arturo's patch effectively gives us more 'digits' to play with by using base
>4, whilst keeping a binary representation.
>
>

your *glitch patch* does NOT work. To see why, examine the table
below. Notice that I diagonalized the odd table entries prior to the
even table entries. My method of diagonalizing fixes a logical flaw
in your argument. You erred, when you let the diagonal string grow
twice as fast as the natural numbers (string pointers) used to index
the diagonal number being constructed. I'm sure you now realize the
absurdity of that. In my table, the odd entries are repressented by
the infinite rational series: 1/6, 7/24, 31/96, 127/384, ... The even
entries are repressented by the infinite rational series: 2/6, 14/24,
62/96, 254/384, ... Notice, for each step in the diagonal
construction, Cantor's number is included, as the previous entry in
the table.

(2/3)(1-(1/2)^(n+1)) (even)
# (1/3)(1-(1/2)^n) (odd) Diagonal Cantor's
--------------------------------------------------------
0 .10
1 .01 .01 .10
2 .1010
3 .0101 01 10
4 .101010
5 .010101 01 10
6 .10101010
7 .01010101 01 10
8 .1010101010
9 .0101010101 01 10
. .
. .
. .10101010101010101010...101010
. .01010101010101010101...010101

Cantor's diagonal number will eventually become a Real number
(completed infinity).

Should we now go back and diagonalize the even table entries? No!
That would be absurd, since Cantor's diagonal number is already
complete (fully determined). It is obvious that Cantor's Diagonal
Method is not applicable, because only half of the table entries
were/(can be) diagonalized.

Nathaniel Deeth
Agge 11

Date Subject Author
12/20/98 Nathaniel Deeth
12/20/98 Ulrich Weigand
12/20/98 Bob Street
12/20/98 Ulrich Weigand
12/22/98 Bob Street
12/22/98 Ulrich Weigand
12/21/98 Nathaniel Deeth
12/21/98 Ulrich Weigand
12/24/98 Nathaniel Deeth
12/24/98 Dik T. Winter
12/25/98 Nathaniel Deeth
12/26/98 Dik T. Winter
12/27/98 jsavard@ecn.ab.ca
12/28/98 Math Icon
12/28/98 David C. Ullrich
12/25/98 Nathaniel Deeth
12/21/98 graham_fyffe@hotmail.com
12/22/98 Nathaniel Deeth
12/24/98 Nathaniel Deeth
12/21/98 David C. Ullrich
12/22/98 Nathaniel Deeth
12/22/98 Bob Street
12/23/98 Nathaniel Deeth
12/24/98 Bob Street
12/25/98 Nathaniel Deeth
12/25/98 Bob Street
12/26/98 Bob Street
12/24/98 Bob Street
12/24/98 Virgil Hancher
12/25/98 Nathaniel Deeth
12/27/98 jsavard@ecn.ab.ca
12/28/98 Robert Harrison
12/22/98 Bob Street
12/22/98 Ulrich Weigand
12/23/98 David C. Ullrich
12/24/98 Nathaniel Deeth
12/24/98 Bob Street
12/25/98 Nathaniel Deeth
12/24/98 David C. Ullrich
12/24/98 Bob Street
12/25/98 Nathaniel Deeth
12/25/98 Nathaniel Deeth
12/25/98 Bob Street
12/25/98 Nathaniel Deeth
12/25/98 Arturo Magidin
12/26/98 Bob Street
12/27/98 Nathaniel Deeth
12/27/98 Nathaniel Deeth
12/28/98 Arturo Magidin
12/28/98 Bob Street
12/30/98 Nathaniel Deeth
12/30/98 Bob Street
12/30/98 Matt Brubeck
12/30/98 Nathaniel Deeth
12/30/98 Bob Street
12/31/98 Nathaniel Deeth
12/31/98 Bob Street
12/31/98 modern life is rubbish
1/3/99 Nathaniel Deeth
1/1/99 standebj@SLU.EDU
1/3/99 Nathaniel Deeth
1/5/99 Bob Street
12/26/98 David C. Ullrich
12/27/98 Nathaniel Deeth
12/28/98 Math Icon
12/28/98 David C. Ullrich
12/25/98 Robert Harrison
12/25/98 Robert Harrison
12/26/98 David C. Ullrich
12/26/98 David C. Ullrich
12/26/98 David C. Ullrich
12/26/98 Bob Street
12/27/98 jsavard@ecn.ab.ca
12/28/98 Nathaniel Deeth
12/28/98 Ronald Bruck
12/28/98 feldmann4350@my-dejanews.com
12/29/98 John Savard
12/30/98 Nathaniel Deeth
12/31/98 Bob Street
12/31/98 Nathaniel Deeth
12/31/98 John Savard
12/31/98 Planar
1/2/99 Bob Street
1/3/99 Nathaniel Deeth
1/5/99 Bob Street
1/3/99 Nathaniel Deeth
1/26/99 Clothes Rod
12/31/98 Planar
1/3/99 Nathaniel Deeth
1/3/99 David C. Ullrich
1/4/99 Bob Street
1/4/99 John Savard
12/31/98 John Savard
1/3/99 Nathaniel Deeth
1/3/99 standebj@SLU.EDU
1/4/99 John Savard
12/31/98 Dave Seaman
1/3/99 Nathaniel Deeth
1/3/99 Ian Storey
1/4/99 Dave Seaman
12/31/98 John Savard
1/3/99 Nathaniel Deeth
1/4/99 John Savard
12/28/98 Bob Street
12/21/98 Nathaniel Deeth
12/21/98 Ulrich Weigand
12/22/98 Nathaniel Deeth
12/22/98 Ulrich Weigand
12/24/98 Nathaniel Deeth
12/24/98 David C. Ullrich
12/28/98 Nathaniel Deeth
12/28/98 Nathaniel Deeth
12/28/98 David C. Ullrich
12/30/98 Nathaniel Deeth
12/31/98 David C. Ullrich
1/1/99 standebj@SLU.EDU
1/3/99 Nathaniel Deeth
1/3/99 standebj@SLU.EDU
12/24/98 Ulrich Weigand
12/28/98 Nathaniel Deeth
12/20/98 David C. Ullrich
12/21/98 Kirby Cook
12/21/98 Nathaniel Deeth
12/21/98 John Starrett
12/21/98 Kirby Cook
12/21/98 John Savard
12/21/98 Jeremy Boden
12/21/98 John Savard
12/22/98 Nathaniel Deeth
12/22/98 Bob Street
12/22/98 John Savard
12/21/98 Barrie Snell
12/22/98 David C. Ullrich
12/23/98 Barrie Snell
12/22/98 Bob Street
12/22/98 zenevsky@wwa.com
12/23/98 Bob Street
12/22/98 John Starrett
12/22/98 Jeremy Boden
12/22/98 Jeremy Boden
12/23/98 Jeremy Boden
12/24/98 David C. Ullrich
12/24/98 John Starrett
12/30/98 Jeremy Boden
12/31/98 brian tivol