On Friday, June 14, 2013 7:46:52 AM UTC-7, muec...@rz.fh-augsburg.de wrote: > 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. >
What? Where did Cantor argue for a linear order of Q by magnitude. Learn some Order Theory, if you can comprehend it.
> > > 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. > Wet and red are not well defined Mathematical terms.
That is required, and it can't be fulfilled and that is why the Well-Ordering of Q respecting magnitude is impossible! The rationals and the naturals are NOT order isomorphic.
How dare we talk of completed infinite, as such is the domain of God. Saint William shall have us all burnt at the stake. > > *) 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. >
This is out of context? What is Dn and what is pn? Also, I'm sure, whatever proof this is from, it's about Cardinals and not Ordinals.
Do you know the difference?
> > That is the condition to be satified. And have satisfied it. > > > > Regards, WM