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From: Stefan.Lucks@uni-weimar.de
Newsgroups: comp.lang.ada
Subject: Re: Is this expected behavior or not
Date: Fri, 5 Apr 2013 16:44:53 +0200
Organization: Bauhaus-Universitaet Weimar
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On Fri, 5 Apr 2013, Dmitry A. Kazakov wrote:

>> Numbers, naturals, integers, rationals and reals, are semantically exact=
ly
>> same except for encoding [representation] and constraints.
>
> A quite common misunderstanding. Structure such as field is not same as a
> subset. To see the difference between R and Z consider the following
> predicate:
>
>   forall x in S exists y such as x=3D1/y  [multiplicative inverse]
>
> This is true for S=3DR and false for S=3DZ.

Fair enough!

But the same is true for N and Z: every in Z has an additive inverse, but=
=20
not every number in N. If the non-existence of a multiplicative inverse=20
would justify different root types for Z and R, why should the=20
non-existence of an additive inverse not justify different root types for=
=20
N and Z (Universal_Positive versus Universal_Integer).

As it turns out, the fact that Naturals and Positives have the same=20
representation as Integers, while Float has a different one, matters more=
=20
than any "mathematical structure" ...





------  I  love  the  taste  of  Cryptanalysis  in  the morning!  ------
     <http://www.uni-weimar.de/cms/medien/mediensicherheit/home.html>
--Stefan.Lucks (at) uni-weimar.de, Bauhaus-Universit=E4t Weimar, Germany--
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