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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