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Topic: Matheology § 285
Replies: 84   Last Post: Jun 15, 2013 6:05 PM

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 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
Re: Matheology § 285
Posted: Jun 15, 2013 4:10 AM

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?

> No.

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.

Regards, WM

Date Subject Author
6/11/13 mueckenh@rz.fh-augsburg.de
6/11/13 Virgil
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6/11/13 Virgil
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