Re: "still unclear on infinite intervals"
> Date: Wed, 25 May 2011 12:07:25 -0500
> From: Ralph Baker Kearfott <rbk5287@xxxxxxxxxxxxx>
> To: Dan Zuras Intervals <intervals08@xxxxxxxxxxxxxx>
> CC: "Corliss, George" <george.corliss@xxxxxxxxxxxxx>,
> stds-1788@xxxxxxxxxxxxxxxxx
> Subject: Re: "still unclear on infinite intervals"
>
> Dan et al,
>
> Wasn't the "still unclear" addressed when motion 3 passed?
> That motion states that intervals are closed and connected
> sets of real numbers. Thus, 0 * (any interval) = 0
> (and infinite bounds are not to be construed to mean
> infinity is included.)
>
> Please correct me if I am wrong or if there are cases not covered
> under that motion.
>
> Baker
>
> P.S. Other extended interval arithmetics define 0*\infty, and
> can also be used. However, we have decided to standardize
> with 0*interval = 0. (personal opinion): it is more important,
> at least in this case, that the programmer know how the system
> defines it, and that the system is the same across platforms,
> than what the actual definition is.
Baker,
Yes, we defined it.
And, yes, I agree that it is more important to have us all
agree than the definition itself.
But my concern is whether or not it is correct in the sense
of inclusive than this particular definition.
This comes up in 754 as well.
The argument is that given a function f(x) such that limit
(x --> 0) f(x) = 0, & a function g(x) such that limit (x --> 0)
g(x) = infinity, we have, of course, that limit (x --> 0)
f(x)*g(x) = anything depending on the details of f() & g().
In 754 we concluded that the only meaningful answer was no
answer at all, namely NaN.
In 1788 we want to return the inclusive interval that is
sure to contain the answer.
I haven't said anything up till now because it seems to me
that any even very narrow interval will have the property
that [0,eps]*[large,infinity] = [0,infinity] which is, no
doubt, correct & inclusive.
And we have defined [+oo,+oo] out of existence so that's
not a problem.
And I shouldn't be worried because [0,0] shouldn't happen
in this case.
But it worries me still.
I guess we have it right & I worry too much.
Never mind.
Its OK.
Dan