Re: .999... ?= 1

From: Eckard Blumschein (blumschein_at_et.uni-magdeburg.de)
Date: 06/03/04 

Date: Thu, 03 Jun 2004 14:09:33 +0100

Robin Chapman wrote:
> The real number 1 remains equal
> to the real number 1,

Well, in IR or Q any exact number is a fictitious one in so far it just
occupies an infinitesimal small range between its neighbours. The chance
to exactly meet a certain value of length approaches zero. One cannot
occupy a large territory without loosing his apartheid. In other words,
Heisenberg's uncertainty principle also holds for numbers. The higher
the resolution the lesser the chance of relevance to a particuzlar
number. There are not just trillions of nearly 1 numbers but infinitely
much.

Incidentally, one can approach the exact number 1 (there is not really a
  real number 1) from below (.9 overbar) as well as from above.
Admittedly, nobody correspondingly writes 1.0 over bar.

>>Nobody can give a concrete epsilon being small
>>enough
>>as not to contain infinitely much rather than infinitely many
>>of different real numbers in between the mentioned two real numbers.
>
>
> Incoherent.

Even if my command of English is shaky in general and not British at
all, my conclusion is perhaps compelling, and shows that there must be
something fundamentally wrong with rather than in the number-based
theory of the continuum.

By the way, my preference for the English of the three lefthanded
presidents in succession Reagan, Bush, and Clinton who studied girls in
Oxford results from the majority of journals demanding American or
Continental style.

E.

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