On Friday, 14 June 2013 10:32:20 UTC+2, Zeit Geist wrote: > > Enumerate the rationals as far as you like. Let n be the largest natural number that ever a human being will think about. Then with 1, 2, ..., n you will have enumerated less than > 10^-10000000000000000000000000000000000 of all rationals. Much less!
> Read what I wrote, dummy.
You want to qualify for the class of Sam Sung and the like?
> For any particular rational, you must be able to find a step where 1/2 all the rationals less than that particular rational, not 1/2 of all rationals, must be placed in its final place.
Why should that be required? In set theory the argument is Cantor's*): If no q remains ouside, then all q will get inside.
> Now change "rational" to "natural". You should ( but probably lake the intellect to ) be able to see the difference.
It is not a matter of intellect, and why should it be wet or red? It is a matter of logic. Your requirement is that at some point already infinitely many rationals must have been enumerated and be in the well-ordered set. It is obviously nonsense to have in the process of enumerating infinitely many.
*) Here is a "proof" by Cantor, showing his principle for a correlation between two infinite sets:
Klar ist zunächst, daß auf diese Weise allen Intervallen Dn bestimmte Punkte pn zugeordnet werden; denn ... es erfährt daher der aus unsrer Regel resultierende Zuordnungsprozeß keinen Stillstand.
That is the condition to be satified. And have satisfied it.