Re: SoA Vs OO

From: Joachim Durchholz (jo_at_durchholz.org)
Date: 07/12/04 

Date: Mon, 12 Jul 2004 12:38:47 +0200

Michael N. Christoff wrote:
> "Joachim Durchholz" <jo@durchholz.org> wrote:
>
>> Michael N. Christoff wrote:
>>
>>> I agree with both you and Willem that depending on language/fpu,
>>> things like 1/0 may be given a special representation. I was
>>> speaking only of the mathematical signifigance of 1/0. However,
>>> in practice it is often is desirable to define results (like
>>> NaN, -oo, +oo) for such mathematically undefined expressions.
>>
>> Let me repeat: 1/0 is most emphatically *not* a "mathematically
>> undefined" expression. It is indeed undefined for real numbers,
>
> If you want to get really abstract, '1' and '0' are just symbols and
> could represent anything (like groups where 1/0 is a quotient group).
> However, I thought it was quite obvious how 1/0 was being
> interpreted, and under that mathematical interpretation it is an
> undefined expression.

Nothing is obvious if mathematics is involved ;-)

And, no, in this particular context (such as IEEE math thrown in), 1/0
can have any number of meanings, including (but not limited to) quite
precise ones.

For example, in IEEE math, 1/0 is equivalent to "the interval of real
numbers between 1-epsilon and 1+epsilon, divided by any number between 0
and +epsilon and rounded to the nearest representable value" - which, in
this case, gives you the value defined as "positive infinity", a "not a
number" value that still has a precisely defined semantics.

Besides, IEEE is "mathematical", even more so than most people realize.
It has a very precisely defined meaning, and even the vagaries are quite
precisely defined.

Further, as I already pointed out, IEEE is not the only possible
interpretation of 1/0. And I'm not speaking of such remote (even if
interesting) things like quotient groups, I'm speaking about interval
arithmetic, symbolic mathematics (where 1/0 has a very precise meaning,
namely that the expression cannot be evaluated, which in turn has very
precise consequences for the evaluation of expressions containing the
value).

1/0 has no useful meaning in real-number arithmetic. However, real
numbers aren't even remotely representable in computers, so this is the
least interesting interpretation of the expression, at least in
computer-related newsgroups.

Saying that "1/0 has no useful meaning" is just FUD. Saying it without
qualifying the context (as has been done in previous messages) even more
so. It's enough to make sure that whatever meaning one assigns to the
expression, it's made clear that this is not 1/0 in the school
mathematics sense - saying "it doesn't make sense" is just repetition of
school dogma.

Just my 2c.
and: 'nuff said.

Regards,
Jo

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