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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: [mg66692] Re: Interval[{a,b}]-Interval[{a,b}] = 0?
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Sat, 27 May 2006 03:51:55 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

On 27 May 2006, at 09:53, Andrzej Kozlowski wrote:

>
>
> It is probably possible to view Mathematica as something like a  
> commutative algebra generated by all well formed expressions,  
> including symbols, strings, names of functions, and so on, with  
> certain relations. But certainly there is no kind of arithmetic of  
> strings.
>>

I guess I should add a correction here. The above will only be true  
if you exclude all expressions involving numerical Intervals and all  
kind of Infinities. My point was of course that the operations Plus  
and Times "work" with almost all mathematica expressions, with 1 as  
the multiplicative and 0 as the additive identity, and that Expand  
will automatically apply the distributive law to any suitable  
expression, whatever the nature of the individual summands or factors.

One could, I dare say, view Mathematica as some kind of abstract  
algebraic structure, but one should not take this view too seriously.  
At least for me, Mathematica is simply a tool, and I do not think it  
is worth implementing any thing purely for the sake of aesthetic  
satisfaction: what counts is whether it has useful computational  
applications. Only when one has such an application in mind it is  
worth implementing it. Please note that I am talking about  
Mathematica, the commercial symbolic algebra program and not  
someone's PhD thesis. Implementing new things in Mathematica costs  
money and ultimately it is we users who pay for it. I would be  
reluctant to pay for additional "features" with do not offer any  
prospects of being useful.

Andrzej Kozlowski


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