Re: Motion P1788/M007.01_NaI
On 2009-08-24 12:36:40 -0400, Michel Hack wrote:
> Vincent Lefevre wrote:
> > No, you can't use the same reasoning because of the rule on the limits:
> > lim_{x -> 0, y -> +oo} x * y
> > doesn't exist (note that here I don't use the extended real numbers).
>
> The problem is that there are two notions of zero in IA:
Note that the context above was IEEE 754, not IA.
> the single point {0}, which is exact, and which is
> idempotent under multiplication with arbitrarily large reals
> and
> an interval containing zero, in which case limit processes
> may indeed be relevant.
No, in IA, 0 is always the real number 0 or the interval {0} = [0,0]
(depending on the context).
> Note that interval arithmetic typically involves IEEE operations on
> endpoints, and that an endpoint of zero should imply that all points
> in the interval have the same sign. Nevertheless I agree that when
> a product of endpoints is of the form 0*oo the indefiniteness of the
> limit may indeed play a role. Arnold Neumaier however seems to have
> good reasons for expecting 0*oo = 0 in this case too.
oo is not a real number (and [+oo,+oo] is not a valid interval),
so that this operation is impossible in IA.
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.org/>
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Work: CR INRIA - computer arithmetic / Arénaire project (LIP, ENS-Lyon)