Re: .999... ?= 1

From: Eckard Blumschein (blumschein_at_et.uni-magdeburg.de)
Date: 06/09/04 

Date: Wed, 09 Jun 2004 14:49:56 +0100

>>>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. For my understanding any decimal number
consists of infinitely much 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. This
does not at all degrade these numbers as long as they constitute a set
of their own where they are easily recognizable. So the quality of a
number depends on where it is embedded.
You can illustrate this easily by marking a line, area, whatever with
black points. They are only visible as long the background is not
entirely black.

Eckard Blumschein

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