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Re: Continuum Hypothesis Solution Posted
Posted:
Apr 22, 1999 9:19 AM
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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
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