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Topic: Continuum Hypothesis Solution Posted
Replies: 44   Last Post: May 1, 1999 5:30 PM

 Messages: [ Previous | Next ]
 Nathaniel Deeth Posts: 548 Registered: 12/4/04
Re: Continuum Hypothesis Solution Posted
Posted: Apr 22, 1999 9:19 AM

Ulrich Weigand wrote:

> Nathan the Great <mad@ashland.baysat.net> writes:
>

> > x = 1 ;the first number
> > N = x ;Set N = {1}
> > Do
> > x = x + 1 ;the successor of x
> > N = N U x ;union element x to Set N
> > Loop

>
> >If/when this algorithm *completes*, N will contain all the natural numbers.
>
> Nope. This algorithm does not terminate. Nevertheless, the set of all
> natural numbers exists. (Who ever said that whether a set does or does
> not exist depends on the existence of an *algorithm* that produces this
> set? Every set produced by an algorithm in this sense will always be
> finite, of course.)

Nathan: My algorithm can construct any number.
Ulrich: Yes. So what?
Nathan: So, I can construct the set of all natural numbers.
Ulrich: No! Why do you say that?
Nathan: Didn't you just say that it can construct every natural number?
Ulrich: No, I agreed that you could construct *any* number.
Nathan: Humm... I can construct *any* number but not *every* number.
Ulrich: Yes, thats correct.
Nathan: Well...since my algorithm constructs the numbers in sequence, if I construct the
last number, I will, in the process, have constructed all the numbers.
Ulrich: Wrong! There is no last number.
Nathan: Oh? Is that why my algorithm never finishes?
Ulrich: uhm.
Nathan: Whats wrong, Dr. Ulrich? Did someone drop a coconut on your head?

Nathan the Great
Age 11

Date Subject Author
4/14/99 Papus
4/15/99 Webster Kehr
4/16/99 Alan Morgan
4/18/99 Webster Kehr
4/16/99 Dave Seaman
4/16/99 Bill Taylor
4/16/99 Nathaniel Deeth
4/16/99 Jake Wildstrom
4/19/99 Sami Aario
4/16/99 Ken Cox
4/19/99 Michel Hack
4/20/99 Nathaniel Deeth
4/20/99 Ulrich Weigand
4/21/99 Nathaniel Deeth
4/21/99 Nathaniel Deeth
4/21/99 Ulrich Weigand
4/21/99 Brian David Rothbach
4/21/99 Virgil Hancher
4/22/99 Nathaniel Deeth
4/22/99 Sami Aario
4/23/99 Nathaniel Deeth
4/25/99 Sami Aario
4/22/99 Ulrich Weigand
4/23/99 Nathaniel Deeth
4/23/99 Ulrich Weigand
4/20/99 Nathaniel Deeth
4/17/99 Papus
4/19/99 Kevin Lacker
4/20/99 Bill Taylor
4/19/99 Andrew Boucher
4/19/99 Kevin Lacker
4/21/99 Andrew Boucher
4/22/99 Keith Ramsay
4/23/99 Andrew Boucher
4/24/99 Keith Ramsay
4/25/99 Andrew Boucher
4/27/99 Bill Taylor
4/27/99 David Petry
4/30/99 Keith Ramsay
5/1/99 Keith Ramsay
4/16/99 Andrew Boucher
4/16/99 Dave Seaman
4/18/99 Webster Kehr
4/19/99 Jeremy Boden
4/19/99 Sami Aario