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MathGroup Archive 2006

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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




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