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Topic: Distinguishability argument x Cantor's arguments?
Replies: 15   Last Post: Jan 9, 2013 4:32 PM

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Posts: 8,833
Registered: 1/6/11
Re: Distinguishability argument x Cantor's arguments?
Posted: Jan 9, 2013 4:16 AM
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In article
WM <> wrote:

> On 9 Jan., 00:15, Virgil <> wrote:
> > In article
> > <>,
> >
> >  WM <> wrote:

> > > On 8 Jan., 14:44, (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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