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MathGroup Archive 2006

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Re: Interval[{a,b}]-Interval[{a,b}] = 0?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg66636] Re: [mg66613] Interval[{a,b}]-Interval[{a,b}] = 0?
  • From: Sseziwa Mukasa <mukasa at jeol.com>
  • Date: Thu, 25 May 2006 02:57:57 -0400 (EDT)
  • References: <200605240701.DAA08477@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

On May 24, 2006, at 3:01 AM, Richard Fateman wrote:

> Is this a bug or a feature?
> Notice that Interval[{-1,1}]-Interval[{-1,1}] is Interval[{-2,2}].

It looks like a bug since Interval[{a,b}]-Interval[{a,b}] should be  
Interval[{a-b,b-a}], the problem is what if a-b and b-a aren't  
defined as in this case?

My guess is the rules for Interval arithmetic are only defined when  
the argument to Interval is a list of two noncomplex numbers.  In  
that sense it's a feature because by definition Mathematica does not  
do Interval arithmetic on arbitrary intervals.

I don't think about intervals much so I'm not familiar with all the  
theory, but reading up on the definition of an Interval it seems they  
are only defined on totally ordered sets.  In Mathematica that would  
seem to restrict their usefulness to the real line anyways, so I  
don't see any problem with the definitions for interval arithmetic as  
they stand.

Regards,

Ssezi


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