On Friday, 14 June 2013 20:30:26 UTC+2, Zeit Geist wrote:
> > > > > Read what I wrote, dummy.
> > > > You want to qualify for the class of Sam Sung and the like?
Then behave and write like a civilized person!
> > 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.
Read what is written, not what want to read. Cantor argued: If no q remains ouside, then all q will get inside. 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. G E O R G C A N T O R, GESAMMELTE ABHANDLUNGEN MATHEMATISCHEN UND PHILOSOPHISCHEN INHALTS, Mit erläuternden Anmerkungen sowie mit Ergänzungen aus dem Briefwechsel Cantor - Dedekind, Herausgegeben von ERNST ZERMELO Nebst einem Lebenslauf Cantors von ADOLF FRAENKEL 1966 GEORG OLMS VERLAGSBUCHHANDLUNG HILDESHEIM, p. 239
> > > 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?
> Wet and red are not well defined Mathematical terms.
Why then did you introduce "lake"? My dictionary gives See or Karminrot.
> That is required, and it can't be fulfilled and that is why the Well-Ordering of Q respecting magnitude is impossible!
That shows that by adding rationals one by one it is impossible to exhaust all of them. Therefore countability is a nonsense notion.
> The rationals and the naturals are NOT order isomorphic.
Neither they are equinumerous.
> Also, I'm sure, whatever proof this is from, it's about Cardinals and not Ordinals. Do you know the difference? > >
That does not play a role in a case where we only have to show that every enumerated rational eventually will be taken into the well-ordered set.