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

*To*: mathgroup at smc.vnet.net*Subject*: [mg66654] Re: [mg66637] Re: Interval[{a,b}]-Interval[{a,b}] = 0?*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Fri, 26 May 2006 04:17:05 -0400 (EDT)*References*: <e510r2$8eg$1@smc.vnet.net> <e514do$96v$1@smc.vnet.net> <200605250658.CAA03721@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

On 25 May 2006, at 15:58, Richard Fateman wrote: > I'm sorry I was not clear in my original note, since several people > seem to think I was objecting to [-1,1] - [-1,1] simplifying to > [-2,2]. > This is universally agreed to be correct in the "reliable computing" > community, for the reason given by Johan, and I certainly > agree with it. > > What is likely to be a bug, in my view, is the treatment of > Interval[{a,b}]-Interval[{a,b}] , and I was just wondering if > anyone could defend simplifying it to 0 as a feature. > > The closest I got was a suggestion that "this is not the right tool". > > One correct answer might be to leave it alone. or maybe > after ascertaining that a,b are real and a<=b , the interval > [-2*a,2*b]. > > The answer 0 not only is wrong, but apparently leads to bugs > in Limit computations, where Interval notation is used /abused. > Note that in Mathematica you will get things like: In[8]:= "a dog" - "a dog" Out[8]= 0 Now, one could also argue that this is a bug, since first of all subtraction of strings (or animals) is not defined and besides there is no reason to assume that the second dog is the same as the first one. Unfortunately Mathematica is very simple minded and when it has no rules for dealing with some object you can always subtract it from itself and get 0 so this fact alone gives you potentially an infinite number of bugs to could complain about! In addition, in Lewis Carroll's "Through The Looking Glass" the question of subtracting a bone from a dog is discussed and a definitive answer provided. I am afraid this answer is also unimplemented in Mathematica, so from this point of view there is another bug, which might result in seriously wrong answers in computations involving dogs and bones. Andrzej Kozlowski

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