[std-interval] Revised document available

[Dr John Pryce]

Guillaume

At 07:14 19/09/06, Guillaume Melquiond wrote:
> > BTW some people feel that the IEEE designers
> > "didn't really intend" Inf to be infinity, but
> > just to mean some finite number too large to
> > represent. But then, why is it that IEEE defines
> > Inf times 0 to be NaN rather than 0?
>
>Because 0 was intended to mean some finite number too small to represent
>(hence its sign) :-).

Touch\'e! However ...

In my view, this shows all the more how important it is to state the 
abstract model underlying an interval system. If our computations are 
to be mathematical proofs based on standard real analysis, it must be 
clear that ABSTRACTLY we are working over the normal reals (or 
extended reals) in which there is just one zero. Some key theorems 
that justify key steps of an interval computation - e.g. Brouwer's 
Theorem or the Intermediate Value Theorem - are essentially 
topological and become false if one alters the topology of the number 
line by including signed zeros that are distinct from each other.

John
Dr John and Mrs Kate Pryce
142 Kingshill Rd
Swindon, Wiltshire SN1 4LW
UK
Tel (+44)1793-331062