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Re: Motion P1788/M007.01_NaI

Michel Hack schrieb:

Vincent Lefevre wrote:

 then it would be much more correct to say "several NaI's"
 than "a NaI with payload".


I agree.


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:
  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.


I think nobody actually working with intervals has the second notion
of zero.



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. 

And this even when the zero is signed.



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.


which are spelled out in Part 7 of the Vienna Proposal.


Arnold Neumaier