Re: More on trits & tetrits... (long)
On 2010-04-10 19:09:49 -0700, Dan Zuras Intervals wrote:
> For the decoration property 'bounded' we will have:
>
> boundedFalse = {There exists x in xx such that f(x)
> is infinite (rounds to infinity)}
>
> boundedTrue = {There exists x in xx such that f(x)
> is finite (rounds to finite number)}
This is not the same "bounded" property as the one that was considered
(which was a level-1 definition, i.e. where f is a function on real
numbers). For instance, let eps be a positive machine number such that
1/eps overflows. What we would like is to regard 1/[0,1] as unbounded
and 1/[eps,1] as bounded. But with your definition, you would get
{ boundedFalse, boundedTrue } is both cases, which is much less
interesting.
> Thus, if one evaluates, for example exp() in single precision
> on the interval [0,100] the answer will be
> {[1,oo],{boundedFalse,boundedTrue}}.
>
> We do not know whether or not an actual pole was encountered.
That's the problem.
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Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
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