Re: The current proposal

[Arnold Neumaier <Arnold.Neumaier@xxxxxxxxxxxx>]

Arnold Neumaier schrieb:
> Nate Hayes schrieb:

> > > > whereas the "ideal" result would be
> > > >
> > > >    (-Inf,b] + (Inf,Inf) = [0,Inf),
> > > >
> > > > assuming the "infinity is number" paradigm where the infinity is not 
> > > > a member of the interval but rather a token for an unbounded real 
> > > > endpoint.
>
> 1/[-1,0] + 1e400 should give in exact arithmetic [-inf,1e400],
> hence with infinity-as-number [-inf,inf] in verified floating
> point arithmetic.
>
> If you don't allow the operation 1/[-1,0] to give the value
> [-inf,0] then the division operation is not appropriate for
> applications to global oto=imization.
>
> But if you assume 1/[-1,0] = [-inf,0], your proposal gives the
> severe underestimate [0,inf].
>
>
>
> > Even the Vienna Proposal says so.
>
> ???
>
> In the Vienna Proposal, Inf is never a real number, and [Inf,Inf]
> is always converted into the empty interval. This is even the case
> in Section 7, where compatibility issues with IEEE directed rounding
> is discussed.

More precisely: The comment in Section 7.6 is not meant to say that Inf
is a real number, but just that the particular assignment of the
particular value +-1 in the specification is motivated by considering 
the limiting case where Inf is replaced by a fixed finite number, and 
then taking this number to infinity. (In case the formulation in the 
Vienna Proposal creates problems to others, it should be replaced.)

Treating Inf as a fixed huge real number would create semantic problems
in many places of the Proposal, and must be discouraged.


Arnold Neumaier