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Subject: Re: why learn C?
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From: Markus E Leypold
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Date: Fri, 13 Apr 2007 02:32:36 +0200
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Date: 2007-04-13T02:32:36+02:00
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Georg Bauhaus <bauhaus@futureapps.de> writes:

> On Thu, 2007-04-12 at 22:33 +0200, Dmitry A. Kazakov wrote:
>>  I can build hardware for floating-point
>> >> numbers with the radix e.
>> > 
>> > Will radix e hardware be digital hardware?
>> 
>> Why not? It is just about representation of numbers in the form
>> 
>> X = sum Xk e**k
>> 
>> That's computable.
>
> Hm. Are you saying that e is computable using digital hardware
> in finite time?

As much as I disklike Dmitry's disgressions in the obscure and
wonderful: But here he is right: A real number representation
  
  (X_n, ... X_0 ..., X_u) means X = sum X_k e**k

has a well defined meaning and those number representations can be
manipulated in finite time by some algorithm (hard or software) that
the operation corresponds to multiplication or addition.

The representations are just a bit long -- but so are those handled by
arbitrary precision libraries like GMP. And of course it tedious to
convert those representations to "normal" floats and most natural
numbers have no (that is no finite representation) in that
system. Fortunately 'e' has a finite representation - '1'.

Regards -- Markus