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Re: Distinguishability of paths of the Infinite Binary tree???
Posted:
Dec 30, 2012 7:29 PM
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On Dec 30, 3:21 pm, Virgil <vir...@ligriv.com> wrote:
> In article
> <fb7fa7ab-bc25-4cb9-9b7c-a073c2fe7...@i2g2000pbi.googlegroups.com>,
> "Ross A. Finlayson" <ross.finlay...@gmail.com> wrote:
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> > On Dec 30, 1:15 pm, Virgil <vir...@ligriv.com> wrote:
> > > In article
> > > <8a425f72-80f2-4aee-9bb9-01f1c6f12...@vb8g2000pbb.googlegroups.com>,
> > > "Ross A. Finlayson" <ross.finlay...@gmail.com> wrote:
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> > > > > requires that they be listable, but one can prove that they are not
> > > > > listable by showing that no list of them can be complete.
> > > > > And no matter how vociferously WM tries to argue otherwise, in standard
> > > > > mathematics that can all be done.
> > > > > --
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> > > > Well, not when "standard" was "pre-Cantorian"
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> > > I used only the present tense which eliminates pre-Cantorianism.
> > > --
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> > Then you shouldn't discount the future
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> I don't, but neither do I pretend to predict it, the way you do.
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> And, as thing stand in the present, standard mathematics supports the
> Cantor diagonal argument and that every Complete Infinite Binary Tree
> which really is a Complete Infinite Binary Tree instead of one of WM's
> corrupted versions of one, must have uncountably many paths.
> --
Until you find applications for transfinite cardinals, it's all
"pretend": pure, abstract mathematics.
Unless you're a Platonist now.
I'm a Platonist: those things are real. Show an application solely
due transfinite cardinals.
And the universe is infinite, and it's real. And: as mathematical
object: it's its own powerset.
And, there may always be more than our "standard" mathematics, but,
existence is that, for what we know it.
Regards,
Ross Finlayson
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