Virgil
Posts:
8,833
Registered:
1/6/11


Re: Distinguishability argument x Cantor's arguments?
Posted:
Jan 9, 2013 4:16 AM


In article <e06a2b9310fa4cac8e5ebe321dfd2308@p17g2000vbn.googlegroups.com>, WM <mueckenh@rz.fhaugsburg.de> wrote:
> On 9 Jan., 00:15, Virgil <vir...@ligriv.com> wrote: > > In article > > <991144926fad4ac1a30eff70224ad...@c14g2000vbd.googlegroups.com>, > > > > WM <mueck...@rz.fhaugsburg.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. > 

