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Re: Matheology § 038
Posted:
Jun 17, 2012 10:17 AM
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On 15 Jun., 19:36, Uergil <Uer...@uer.net> wrote:
> In article
> <a709d9b2-7cd9-4c7c-b9f1-4b07bbb4d...@n5g2000vbb.googlegroups.com>,
>
>
>
>
>
> WM <mueck...@rz.fh-augsburg.de> wrote:
> > On 15 Jun., 01:56, Uergil <Uer...@uer.net> wrote:
> > > In article
> > > <f7304e1b-1ddb-4e44-be50-3ed5d30e3...@d6g2000vbe.googlegroups.com>,
>
> > > WM <mueck...@rz.fh-augsburg.de> wrote:
> > > > On 14 Jun., 21:59, Uergil <Uer...@uer.net> wrote:
>
> > > > > > > Evidently you misunderstood the question. The question is:
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> > > > > > Are there uncountably many real numbers.
> > > > > > The answer is a resounding: No.
>
> > > > > Then lets see WM count them!
>
> > > > That cannot be done, because they are not available. It is a
> > > > potentially infinite set. The completely absurd assumption that all
> > > > were "there" (because God knows them) is really ridiculous.
>
> > > > > > No. It is a gross mistake to assume that the rational numbers could be
> > > > > > counted.
>
> > > > > That depends on one's definition of "counting".
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> > > > No, it depends on the correct understanding of limits.
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> > > Then WM's definition of 'counting' is grossly different from any
> > > standard meaning in mathemtics.
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> > > Because by a more standard mathematical definition of counting, the set
> > > of rationals not only CAN be counted it frequently HAS BEEN counted.
>
> > > A Google search for "counting the rationals" came up with 174,000 hits
> > > in 0.61 seconds, including:
>
> > You can do better. Simply try it.
> > Number of angels:
> > 198.000.000 hits in 0.2 s.
>
> Except that many of the "counting the rationals" hits include
> mathematically valid proofs of the countability of the rationals, i.e.
> well-orderings of the rationals that are order-isomorphic to the
> standard well-ordering of the naturals.
>
> Does WM claim that any of those "numberings" of the angels are
> mathematically valid?
With absolute certainty they are not less valid than enumerations of
the rationals.
Regads, WM
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