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

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Ulrich Weigand

Posts: 72
Registered: 12/12/04
Re: Nathan counts the powerset
Posted: Dec 22, 1998 6:39 AM
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Mike Deeth <mad@ashland.baysat.net> writes:

>Ulrich Weigand wrote:

>> A set is finite if there is a bijection from the set to some integer.
>> A set is infinite if it is not finite. Where's the problem?


>In a previous post I showed a bijection between the members of the powerset of
>natural numbers and the natural numbers. Several peaple commented that, although the
>bijection was correct, and mapped EVERY finite subset, it missed all the infinite
>subsets. ie. Which number corresponds with the set of ALL even numbers? I produce
>the number "...10101010".


This is not a number; its an string of digits. Now finite strings of digits
are usually interpreted as representations of natural numbers. But this does
not work for infinite strings of digits. If you don't agree, please tell us
to which natural number the string given above corresponds ...

>Now they said, "if that number is infinite, its not a
>natural number. If that number is finite, it doesn't map the infinite sets" There
>appears to be no way out of this, catch 22, situation.


That's a somewhat strange way to state it; every natural number is finite
(you might say that's the definition of 'finite'), and again by definition
no infinite set is bijective to any finite set.

>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, ... }



There is no last row. That would contain the 'last' natural number, but
according to the Peano axioms which you are so fond of, every natural number
has a successor, hence there is no last natural number.

Your table contains in the left column all natural numbers, and in the
right column a bunch of finite sets. No single infinite set occurs.


>Hint: there are no infinite sets.

Oh, really :-) Might I ask according to which axiomatic foundation you
decide about existence or non-existence of sets?

--
Ulrich Weigand,
IMMD 1, Universitaet Erlangen-Nuernberg,
Martensstr. 3, D-91058 Erlangen, Phone: +49 9131 85-7688






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
Bob Street
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
Arturo Magidin
12/28/98
Read Re: Nathan counts the powerset
Bob Street
12/30/98
Read Re: Nathan counts the powerset
Nathaniel Deeth
12/30/98
Read Re: Nathan counts the powerset
Bob Street
12/30/98
Read Re: Nathan counts the powerset
Matt Brubeck
12/30/98
Read Re: Nathan counts the powerset
Nathaniel Deeth
12/30/98
Read Re: Nathan counts the powerset
Bob Street
12/31/98
Read Re: Nathan counts the powerset
Nathaniel Deeth
12/31/98
Read Re: Nathan counts the powerset
Bob Street
12/31/98
Read Re: Nathan counts the powerset
modern life is rubbish
1/3/99
Read Re: Nathan counts the powerset
Nathaniel Deeth
1/1/99
Read Re: Nathan counts the powerset
standebj@SLU.EDU
1/3/99
Read Re: Nathan counts the powerset
Nathaniel Deeth
1/5/99
Read Re: Nathan counts the powerset
Bob Street
12/26/98
Read Re: Nathan counts the powerset
David C. Ullrich
12/27/98
Read Re: Nathan counts the powerset
Nathaniel Deeth
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
Robert Harrison
12/25/98
Read Re: Nathan counts the powerset
Robert Harrison
12/26/98
Read Re: Nathan counts the powerset
David C. Ullrich
12/26/98
Read Re: Nathan counts the powerset
David C. Ullrich
12/26/98
Read Re: Nathan counts the powerset
David C. Ullrich
12/26/98
Read Re: Nathan counts the powerset
Bob Street
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
Read Re: Nathan counts the powerset
feldmann4350@my-dejanews.com
12/29/98
Read Re: Nathan counts the powerset
John Savard
12/30/98
Read Re: Nathan counts the powerset
Nathaniel Deeth
12/31/98
Read Re: Nathan counts the powerset
Bob Street
12/31/98
Read Re: Nathan counts the powerset
Nathaniel Deeth
12/31/98
Read Re: Nathan counts the powerset
John Savard
12/31/98
Read Re: Nathan counts the powerset
Planar
1/2/99
Read Re: Nathan counts the powerset
Bob Street
1/3/99
Read Re: Nathan counts the powerset
Nathaniel Deeth
1/5/99
Read Re: Nathan counts the powerset
Bob Street
1/3/99
Read Re: Nathan counts the powerset
Nathaniel Deeth
1/26/99
Read Re: Nathan counts the powerset
Clothes Rod
12/31/98
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Planar
1/3/99
Read Re: Nathan counts the powerset
Nathaniel Deeth
1/3/99
Read Re: Nathan counts the powerset
David C. Ullrich
1/4/99
Read Re: Nathan counts the powerset
Bob Street
1/4/99
Read Re: Nathan counts the powerset
John Savard
12/31/98
Read Re: Nathan counts the powerset
John Savard
1/3/99
Read Re: Nathan counts the powerset
Nathaniel Deeth
1/3/99
Read Re: Nathan counts the powerset
standebj@SLU.EDU
1/4/99
Read Re: Nathan counts the powerset
John Savard
12/31/98
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Dave Seaman
1/3/99
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Nathaniel Deeth
1/3/99
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Ian Storey
1/4/99
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Dave Seaman
12/31/98
Read Re: Nathan counts the powerset
John Savard
1/3/99
Read Re: Nathan counts the powerset
Nathaniel Deeth
1/4/99
Read Re: Nathan counts the powerset
John Savard
12/28/98
Read Re: Nathan counts the powerset
Bob Street
12/21/98
Read Re: Nathan counts the powerset
Nathaniel Deeth
12/21/98
Read Re: Nathan counts the powerset
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
Read Re: Nathan counts the powerset
Nathaniel Deeth
12/24/98
Read Re: Nathan counts the powerset
David C. Ullrich
12/28/98
Read Re: Nathan counts the powerset
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
Read Re: Nathan counts the powerset
Ulrich Weigand
12/28/98
Read Re: Nathan counts the powerset
Nathaniel Deeth
12/20/98
Read Re: Nathan counts the powerset
David C. Ullrich
12/21/98
Read Re: Nathan counts the powerset
Kirby Cook
12/21/98
Read Re: Nathan counts the powerset
Nathaniel Deeth
12/21/98
Read Re: Nathan counts the powerset
John Starrett
12/21/98
Read Re: Nathan counts the powerset
Kirby Cook
12/21/98
Read Re: Nathan counts the powerset
John Savard
12/21/98
Read Re: Nathan counts the powerset
Jeremy Boden
12/21/98
Read Re: Nathan counts the powerset
John Savard
12/22/98
Read Re: Nathan counts the powerset
Nathaniel Deeth
12/22/98
Read Re: Nathan counts the powerset
Bob Street
12/22/98
Read Re: Nathan counts the powerset
John Savard
12/21/98
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Barrie Snell
12/22/98
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David C. Ullrich
12/23/98
Read Re: Nathan counts the powerset
Barrie Snell
12/22/98
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Bob Street
12/22/98
Read Re: Nathan counts the powerset
zenevsky@wwa.com
12/23/98
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Bob Street
12/22/98
Read Re: Nathan counts the powerset
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
Read Re: Nathan counts the powerset
Jeremy Boden
12/31/98
Read Re: Nathan counts the powerset
brian tivol

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