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Re: Unbounded intervals

Baker Kearfott wrote:

And I don't think the concept of overflow should be in Level 1,
as there is no such concept in mathematical intervals.


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I don't think anyone wants the infinity to be part of an interval.
Nate wants to replace unbounded intervals by something else, but
this is unclear, as he said that this is equivalent to unbounded
intervals. So, I don't see the point of such a change.



So, do I take it that there would be no consequence to how we
actually end up defining the operations?


For the representation, using the infinity symbol is fine for me.
This is standard and well-known.



Then, is it correct that the contention is merely describing
how we think about it and what notation we use, and not what
the actual operations will be?


This has been one of my observations from the beginning:

Nate Hayes wrote on 4/8/2012:

From a practical perspective: for any and all inverval arithmetic
operations and applications, if you simply replace +Inf from the current
P1788 model with +OVR, then the interval arithmetic formulas in Motion 5
are still completely accurate and unchanged. The main difference is in the
formality of the underlying mathematical definitions about how such
results are obtained. In the new model, all Level 1 intervals are closed
and bounded (compact).


At Level 3 a vendor could choose to use IEEE 754 infinity as representation
for overflow, as Dan said. But we should not lump these concepts together at
Level 1 and Level 2 as IEEE 754 has done. At least that is my position.

Vincent says he doesn't see the point of overflow though in the course of
disussion it seems to me he has changed his position from unbounded
intervals are "essential" to "they make algorithms more easy to define at
Level 1." But both statements are not true so now it appears the reason is
"there is no overflow in mathematical intervals," a claim I've never even
asserted. In his retorts to my last e-mail I've been accused of not paying attention, but it seems perhaps this is his problem too. So I think this discussion on that note has degenerated into a level of obfuscation that makes it no longer useful. 

I had mentioned earlier we are still working on a model for overflow and I
would present a paper when we have time to finish it.

Nate