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

**References**:**Interval[{a,b}]-Interval[{a,b}] = 0?***From:*"Richard Fateman" <fateman@cs.berkeley.edu>