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From: "Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de>
Newsgroups: comp.lang.ada
Subject: Re: Is this expected behavior or not
Date: Fri, 5 Apr 2013 16:19:04 +0200
Organization: cbb software GmbH
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Date: 2013-04-05T16:19:04+02:00
List-Id: <comp.lang.ada>

On Fri, 5 Apr 2013 14:49:41 +0200, Stefan.Lucks@uni-weimar.de wrote:

> On Fri, 5 Apr 2013, Stefan.Lucks@uni-weimar.de wrote:
> 
>> On Fri, 5 Apr 2013, Dmitry A. Kazakov wrote:
>>
>>> Unicode strings, all of them, are semantically exactly same except for 
>>> encoding [representation] and constraints put on the code point set.
>>
>> N is a subset of Z is a subset of Q is a subset of R.

Depends on construction. The proper statement is that Q has a subset
equivalent to Z and R has a subset equivalent to Q.

>> Furthermore, each "X is a subset of Y" relationship implies that any 
>> operation possible in X is also possible in Y, including comparisons.
> 
> What I meant to write:
> 
> Numbers, naturals, integers, rationals and reals, are semantically exactly 
> 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=1/y  [multiplicative inverse]

This is true for S=R and false for S=Z.

-- 
Regards,
Dmitry A. Kazakov
http://www.dmitry-kazakov.de