Extended real arithmetic (was Re: inf - inf = 0 ??)



  On 9/13/2010 5:52 AM, Stavros Macrakis wrote:
> Exactly.
>
> On 2010-09-13, Viktor T. Toth<vttoth at vttoth.com>  wrote:
>> Correct me if I am mistaken but I think a basic assumption behind
>> simplification is that any unevaluated symbol represents a finite,
>> determinate quantity.

You could make this assumption, and perhaps the simplifier implicitly 
makes this assumption, but
it is an incorrect assumption.  For example, assume you allow the 
expression x*tan(x).
Now let x=pi/2.   You have   finite * (+- infinity).

If you make the assumption that any expression (not just symbols) cannot 
be indeterminate or infinite,
then the simplifier probably "works".

That is, however, like curing world hunger by assuming everyone has 
enough food to eat.

RJF


>>   Hence, you're allowed to simplify 0*x as 0, even
>> though 0*inf is definitely not 0, because the value of x, whatever it might
>> be (real number, complex number, vector, matrix, operator, quaternion,
>> etc.), is not infinite or indeterminate.
>>
>>
>> Viktor
>>
>>
>>
...