
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

