Re: The current proposal
On 2009-02-26 12:08:59 -0500, Ian McIntosh wrote:
> VL> "Infinity as number" is buggy. For instance, with the above point of
> VL> view, if F(x) = (x+1)-x, then F(Inf) = (Inf+1)-Inf = Inf-Inf = 0.
>
> Under IEEE 754, F(Inf) = (Inf+1)-Inf = Inf-Inf = NaN, not 0.
But you changed the rules. Under IEEE 754, is *not* like a real number
(what Nate says by "a token for an unbounded real number" -- which is
IMHO non-sense). You should read the context:
> >> This value is not even properly defined in many cases,
> >> such as when F(x)=x-x or F(x)=(x-1)/(x+1) and A=[0,inf].
> >
> > If "infinity as number" is true, i.e., if the infinity is not a
> > member of the interval but rather a token for an unbounded real
> > number, then it is properly defined:
> >
> > F(Inf)=Inf-Inf=0
> > F(Inf)=(Inf-1)/(Inf+1)=Inf/Inf=1
> >
> > Nate Hayes
> > Sunfish Studio, LLC
I'm just saying that the definitions proposed by Nate, which seem
to be OK for F(x)=x-x and F(x)=(x-1)/(x+1), are buggy because for
other functions, e.g. F(x) = (x+1)-x, the obtained result is clearly
incorrect.
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.org/>
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Work: CR INRIA - computer arithmetic / Arenaire project (LIP, ENS-Lyon)