Virgil
Posts:
4,482
Registered:
1/6/11
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Re: Objection to Cantor's Theorem
Posted:
Jul 28, 2012 7:16 PM
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In article <jv1rd0$slh$2@speranza.aioe.org>,
"LudovicoVan" <julio@diegidio.name> wrote:
> "David C. Ullrich" <ullrich@math.okstate.edu> wrote in message
> news:0s2818pddlcgia1uj8v59cgduu837fht30@4ax.com...
> > On Sat, 28 Jul 2012 00:53:05 +0100, "LudovicoVan"
> > <julio@diegidio.name> wrote:
> >>"hagman" <google@von-eitzen.de> wrote in message
> >>news:828340c5-a1fb-46db-aa8c-32408eea3a91@n5g2000vbb.googlegroups.com...
> >>> On 23 Jul., 01:40, "LudovicoVan" <ju...@diegidio.name> wrote:
> >>>> "hagman" <goo...@von-eitzen.de> wrote in message
> >>>> news:94ddf509-18ce-4522-a104-bd298dc247ff@googlegroups.com...> Am
> >>>> Samstag, 21. Juli 2012 02:32:52 UTC+2 schrieb LudovicoVan:
> >>>> <snipped>
> >>>>
> >>>> >> I am most probably not using the standard axioms, but I do not have
> >>>> >> a
> >>>> >> list
> >>>> >> of axioms ready, yet. -- What would be the minimal set of axioms
> >>>> >> to
> >>>> >> support Cantor's diagonal argument?
> >>>>
> >>>> > Let's try to make a readable presentation:
> >>>>
> >>>> You present Cantor's Theorem. And, it's very welcome...
> >>>>
> >>>> > (1) A u: u e C <-> u e A & A z: (<u,z> e f -> ~(u e z))
> >>>>
> >>>> So, to define C we quantify over all sets.
> >>>
> >>> I do not define C.
> >>
> >>Must be my French again, but the point remains: "A z" makes the
> >>impredicativity I was after. (Please correct me if I am mistaken.)
> >
> > You are mistaken.
>
> No correction, no mistake.
LV is too dim to recognize his own errors,even when they are pointed out
to him.
>
> >>Impredicativity is when the "description" of an entity depends on the
> >>totality of entities to which it belongs.
> >
> > Perhaps. That's very different from saying the description
> > of an entity depends on the totality of entities which
> > belong to it.
>
> <http://en.wikipedia.org/wiki/Impredicativity>
>
> -LV
>
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