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

 Messages: [ Previous | Next ]
 Bob Street Posts: 63 Registered: 12/12/04
Re: Nathan counts the powerset
Posted: Dec 24, 1998 10:24 AM

Mike Deeth wrote in message <3681B99D.66997C67@ashland.baysat.net>...
>
>
>The table below shows a bijection between a Natural number and a Set with

the
>same
>number of members. None can doubt this bijection continues into the

infinite.
>Lets say that the last row of the table contains the infinite set of all
natural
>
>numbers. What natural number is it in bijection with? (Remember, the

number
>must
>be a Natural)
>
> N Set-of-N
>---------------------
> 1 {1}
> 2 {1,2}
> 3 {1,2,3}
> 4 {1,2,3,4}
> 5 {1,2,3,4,5}
> . .
> . .
> . .
> ? {1,2,3, ... }
>
>

That's a bijection between the set of *finite* sets of the form {1, 2, 3,
..., n} and the set of natural numbers. Whilst it 'continues into the
infinite', at no point does it map an infinite set to an infinite natural.
All the Set-of-N things in your table are finite sets. All Natural numbers
are finite.

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