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From: "Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de>
Subject: Re: and then... (a curiosity)
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Date: Thu, 4 Sep 2008 18:33:30 +0200
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On Thu, 4 Sep 2008 14:12:57 +0200, stefan-lucks@see-the.signature wrote:

> BTW, why do you think that an exception, such as a Constraint_Error, 
> should logically count as a contradiction? 
> 
> Dividing something by zero is undefined, not a contradiction.

Undefined is a too vague term.

When a mathematician tells that X/0 > 100 is undefined he usually means
that X/0 > 100 has no interpretation.

But "X/0 > 100 = _|_" has an interpretation. Namely: m(X/0 in ]100,oo[)=1,
m(X/0 not in = ]100,oo[)=1. I.e. it is both possible for X/0 be in ]100,oo[
or in its complement. This is uncertainty.

"X/0 > 100 = T" means that neither is possible (contradiction). This
"contradiction" is closer to an intuitive understanding of X/0 > 100, yet
it is not the standard mathematical meaning of, which is that X/0 > 100 is
not a formula at all.

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