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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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 Virgil Posts: 8,833 Registered: 1/6/11
Re: Distinguishability argument x Cantor's arguments?
Posted: Jan 9, 2013 3:24 PM

In article
WM <mueckenh@rz.fh-augsburg.de> wrote:

> 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.

Then no number is "given" by a word until that word as been given the
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.

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

So that, at least in your mind, the collected works of Shakespeare are
just one word?
> >
> > > 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.

What I have used is a finite initial segment for the infinite sequence
of characters representing pi, a sequence of characters which is not
even a number unless I intend it to be.

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.

One can finitely define infinite processes, like Archimedes method of
approximating pi, but that does not make those processes finite.
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