Re: Unbounded intervals
On 2012-04-26 07:48:58 -0500, Ralph Baker Kearfott wrote:
> Just reading the on-going discussion (and perhaps missing a
> few posts) without reviewing, I'm beginning to lose track
> of where this discussion is headed with regard to what we
> will eventually specify (or not specify) in the standard,
> or how we will word the standard. I admit the discussion
> is interesting, can someone perhaps summarize? What I have
> gathered so far is there is contention about whether there
> should be a concept of infinity, or just a concept of
> overflow, at level 1.
Actually the concept of infinity (as an element of some set) and
the concept of unbounded intervals are different concepts. You can
specify unbounded intervals without using the concept of infinities;
for instance, I = { x in R | x >= 1 } is an unbounded interval.
However using infinities allows one to avoid the need of
distinguishing both kinds of intervals.
And I don't think the concept of overflow should be in Level 1,
as there is no such concept in mathematical intervals.
> Suppose we have some symbol, say
> \aleph, to represent this (be it infinity or overflow).
> Can someone explain (or work through, or review, e.g.
> by presenting two contrasting tables) how it will affect
> the actual operations, whether we think of \aleph as
> infinity or overflow? P-1788 has already decided that
> infinity is not an actual element of an interval, but
> the symbol can be used to represent an unbounded interval,
> and there are consequences of this decision in the result
> of operations.
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.
For the representation, using the infinity symbol is fine for me.
This is standard and well-known.
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
100% accessible validated (X)HTML - Blog: <http://www.vinc17.net/blog/>
Work: CR INRIA - computer arithmetic / AriC project (LIP, ENS-Lyon)