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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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 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
Re: Distinguishability argument x Cantor's arguments?
Posted: Jan 9, 2013 7:10 AM

On 9 Jan., 10:16, Virgil <vir...@ligriv.com> wrote:

> > 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.

Just so.

>
> > 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.

Every finite string of symbols is a word. This includes Shakespeares
collected works as well as the number 1.
>
> > 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.

But you are not bright enough to understand that you have used a
rational number defined by a single word. And if you meant it as an
approximation of pi that eventually has to be improved, then you need
a definition of pi, i.e., a finitely defined way to obtain better
approximations.

Regards, WM