Virgil
Posts:
4,661
Registered:
1/6/11
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Re: Distinguishability argument x Cantor's arguments?
Posted:
Jan 9, 2013 4:16 AM
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In article
<e06a2b93-10fa-4cac-8e5e-be321dfd2308@p17g2000vbn.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 9 Jan., 00:15, Virgil <vir...@ligriv.com> wrote:
> > In article
> > <99114492-6fad-4ac1-a30e-ff70224ad...@c14g2000vbd.googlegroups.com>,
> >
> > WM <mueck...@rz.fh-augsburg.de> wrote:
> > > On 8 Jan., 14:44, mstem...@walkabout.empros.com (Michael Stemper)
> >
> > > > However, ANY real can be distinguished from ANY other by SOME finite
> > > > initial segment of its decimal, or other base, representation.
> >
> > > The problem is not distinguishing given reals, but how reals can
> > > uniquely by *given*. That requires a finite definition. But I am
> > > afraid that you don't even understand what that means.
>
> > A set is determined by any rule for distinguishing whether a test object
> > is or is not a member.
>
> A real number is determined or "given" by a unique word.
No number is given by a single word until that word has been defined as
meaning some number.
> Otherwise it
> could not be used.
Many, if not most, numbers are referred to by numerals which are at
least grammatically more like phrases rather than single words.
> And it was not possible to compare some finite
> initial segment of it with something else.
I can compare 3.14159 with a lot of things. That WM confesses his
inability to do so is just a measure of his general inabilities.
>
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