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

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Nathaniel Deeth

Posts: 548
Registered: 12/4/04
Re: Nathan counts the powerset
Posted: Dec 30, 1998 5:29 PM
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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>,
>>> Mike Deeth <mad@ashland.baysat.net> wrote:

>>> >
>>> >

>> (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
Read Nathan counts the powerset
Nathaniel Deeth
12/20/98
Read Re: Nathan counts the powerset
Ulrich Weigand
12/20/98
Read Re: Nathan counts the powerset
Bob Street
12/20/98
Read Re: Nathan counts the powerset
Ulrich Weigand
12/22/98
Read Re: Nathan counts the powerset
Bob Street
12/22/98
Read Re: Nathan counts the powerset
Ulrich Weigand
12/21/98
Read Re: Nathan counts the powerset
Nathaniel Deeth
12/21/98
Read Re: Nathan counts the powerset
Ulrich Weigand
12/24/98
Read Re: Nathan counts the powerset
Nathaniel Deeth
12/24/98
Read Re: Nathan counts the powerset
Dik T. Winter
12/25/98
Read Re: Nathan counts the powerset
Nathaniel Deeth
12/26/98
Read Re: Nathan counts the powerset
Dik T. Winter
12/27/98
Read Re: Nathan counts the powerset
jsavard@ecn.ab.ca
12/28/98
Read Re: Nathan counts the powerset
Math Icon
12/28/98
Read Re: Nathan counts the powerset
David C. Ullrich
12/25/98
Read Re: Nathan counts the powerset
Nathaniel Deeth
12/21/98
Read Re: Nathan counts the powerset
graham_fyffe@hotmail.com
12/22/98
Read Re: Nathan counts the powerset
Nathaniel Deeth
12/24/98
Read Re: Nathan counts the powerset
Nathaniel Deeth
12/21/98
Read Re: Nathan counts the powerset
David C. Ullrich
12/22/98
Read Re: Nathan counts the powerset
Nathaniel Deeth
12/22/98
Read Re: Nathan counts the powerset
Bob Street
12/23/98
Read Re: Nathan counts the powerset
Nathaniel Deeth
12/24/98
Read Re: Nathan counts the powerset
Bob Street
12/25/98
Read Re: Nathan counts the powerset
Nathaniel Deeth
12/25/98
Read Re: Nathan counts the powerset
Bob Street
12/26/98
Read Re: Nathan counts the powerset
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12/24/98
Read Re: Nathan counts the powerset
Bob Street
12/24/98
Read Re: Nathan counts the powerset
Virgil Hancher
12/25/98
Read Re: Nathan counts the powerset
Nathaniel Deeth
12/27/98
Read Re: Nathan counts the powerset
jsavard@ecn.ab.ca
12/28/98
Read Re: Nathan counts the powerset
Robert Harrison
12/22/98
Read Re: Nathan counts the powerset
Bob Street
12/22/98
Read Re: Nathan counts the powerset
Ulrich Weigand
12/23/98
Read Re: Nathan counts the powerset
David C. Ullrich
12/24/98
Read Re: Nathan counts the powerset
Nathaniel Deeth
12/24/98
Read Re: Nathan counts the powerset
Bob Street
12/25/98
Read Re: Nathan counts the powerset
Nathaniel Deeth
12/24/98
Read Re: Nathan counts the powerset
David C. Ullrich
12/24/98
Read Re: Nathan counts the powerset
Bob Street
12/25/98
Read Re: Nathan counts the powerset
Nathaniel Deeth
12/25/98
Read Re: Nathan counts the powerset
Nathaniel Deeth
12/25/98
Read Re: Nathan counts the powerset
Bob Street
12/25/98
Read Re: Nathan counts the powerset
Nathaniel Deeth
12/25/98
Read Re: Nathan counts the powerset
Arturo Magidin
12/26/98
Read Re: Nathan counts the powerset
Bob Street
12/27/98
Read Re: Nathan counts the powerset
Nathaniel Deeth
12/27/98
Read Re: Nathan counts the powerset
Nathaniel Deeth
12/28/98
Read Re: Nathan counts the powerset
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12/28/98
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12/30/98
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Nathaniel Deeth
12/30/98
Read Re: Nathan counts the powerset
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12/30/98
Read Re: Nathan counts the powerset
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12/30/98
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12/30/98
Read Re: Nathan counts the powerset
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12/31/98
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12/31/98
Read Re: Nathan counts the powerset
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12/31/98
Read Re: Nathan counts the powerset
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1/3/99
Read Re: Nathan counts the powerset
Nathaniel Deeth
1/1/99
Read Re: Nathan counts the powerset
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1/3/99
Read Re: Nathan counts the powerset
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1/5/99
Read Re: Nathan counts the powerset
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12/26/98
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12/27/98
Read Re: Nathan counts the powerset
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12/28/98
Read Re: Nathan counts the powerset
Math Icon
12/28/98
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12/25/98
Read Re: Nathan counts the powerset
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12/25/98
Read Re: Nathan counts the powerset
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12/26/98
Read Re: Nathan counts the powerset
David C. Ullrich
12/26/98
Read Re: Nathan counts the powerset
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12/26/98
Read Re: Nathan counts the powerset
David C. Ullrich
12/26/98
Read Re: Nathan counts the powerset
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12/27/98
Read Re: Nathan counts the powerset
jsavard@ecn.ab.ca
12/28/98
Read Re: Nathan counts the powerset
Nathaniel Deeth
12/28/98
Read Re: Nathan counts the powerset
Ronald Bruck
12/28/98
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feldmann4350@my-dejanews.com
12/29/98
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12/30/98
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Nathaniel Deeth
12/31/98
Read Re: Nathan counts the powerset
Bob Street
12/31/98
Read Re: Nathan counts the powerset
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12/31/98
Read Re: Nathan counts the powerset
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12/31/98
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1/2/99
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1/3/99
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1/5/99
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1/3/99
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1/26/99
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12/31/98
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1/3/99
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Nathaniel Deeth
1/3/99
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David C. Ullrich
1/4/99
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1/4/99
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John Savard
12/31/98
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1/3/99
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Nathaniel Deeth
1/3/99
Read Re: Nathan counts the powerset
standebj@SLU.EDU
1/4/99
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John Savard
12/31/98
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1/3/99
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1/3/99
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1/4/99
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12/31/98
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John Savard
1/3/99
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Nathaniel Deeth
1/4/99
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John Savard
12/28/98
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Bob Street
12/21/98
Read Re: Nathan counts the powerset
Nathaniel Deeth
12/21/98
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Ulrich Weigand
12/22/98
Read Re: Nathan counts the powerset
Nathaniel Deeth
12/22/98
Read Re: Nathan counts the powerset
Ulrich Weigand
12/24/98
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Nathaniel Deeth
12/24/98
Read Re: Nathan counts the powerset
David C. Ullrich
12/28/98
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Nathaniel Deeth
12/28/98
Read Re: Nathan counts the powerset
Nathaniel Deeth
12/28/98
Read Re: Nathan counts the powerset
David C. Ullrich
12/30/98
Read Re: Nathan counts the powerset
Nathaniel Deeth
12/31/98
Read Re: Nathan counts the powerset
David C. Ullrich
1/1/99
Read Re: Nathan counts the powerset
standebj@SLU.EDU
1/3/99
Read Re: Nathan counts the powerset
Nathaniel Deeth
1/3/99
Read Re: Nathan counts the powerset
standebj@SLU.EDU
12/24/98
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Ulrich Weigand
12/28/98
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Nathaniel Deeth
12/20/98
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David C. Ullrich
12/21/98
Read Re: Nathan counts the powerset
Kirby Cook
12/21/98
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Nathaniel Deeth
12/21/98
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John Starrett
12/21/98
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Kirby Cook
12/21/98
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John Savard
12/21/98
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Jeremy Boden
12/21/98
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John Savard
12/22/98
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Nathaniel Deeth
12/22/98
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Bob Street
12/22/98
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John Savard
12/21/98
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Barrie Snell
12/22/98
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David C. Ullrich
12/23/98
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Barrie Snell
12/22/98
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Bob Street
12/22/98
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zenevsky@wwa.com
12/23/98
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Bob Street
12/22/98
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John Starrett
12/22/98
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Jeremy Boden
12/22/98
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Jeremy Boden
12/23/98
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Jeremy Boden
12/24/98
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David C. Ullrich
12/24/98
Read Re: Nathan counts the powerset
John Starrett
12/30/98
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Jeremy Boden
12/31/98
Read Re: Nathan counts the powerset
brian tivol

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