Re: .999... ?= 1

From: Virgil (ITSnetNOTcom/virgil_at_COMCAST.com)
Date: 06/09/04 

Date: Wed, 09 Jun 2004 12:48:13 -0600

In article <40C71584.3060607@et.uni-magdeburg.de>,
 Eckard Blumschein <blumschein@et.uni-magdeburg.de> wrote:

> >>>On the contrary. A number is not represented by a finite series but by
> >>>an infinite one. This makes the difference.
> >>>
> >>>Eckard Blumschein
> >>
> >>Actually, each of the natural numbers, including zero in modern usage,
> >>is represented by a finite series of digits, at least in standard
> >>decimal notation.
> >
> Acid Pooh wrote:>
> > Sure, but every real (and hence, every integer) can be represented as
> > the limit of a Cauchy sequence of rationals, and hence can be
> > decomposed into the limit of partial sums of an appropriate series.
> > Moreover, there are infinitely many series which converge to any given
> > real number.
>
> Standard decimal notation is perhaps a bit misleading in so far it omits
> .0 overbar for convenience.

It only misleads those who do not understand it. Decimal notation for
integers, such as zero, does not even imply overbars.

 For my understanding any decimal number
> consists of infinitely much digits.

Then you understand wrongly. To start with, decimals are numerals, not
numbers. And there are infinitely many numbers, even excluding the
integers, whose decimal numerals do not require infinitely many digits.

That's why I conclude: Even natural
> numbers are quite irrelevant when embedded in c because they are
> indiscriminable from the overwhelming adjacent rest of continuum.
 
 I do not find any dictionary entries for "indiscriminable". Perhaps it
is merely an artifact of Eckwhatever's internal incoherence.

Or perhaps Eckwhatever just needs his discerner adjusted.

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