Lennart Augustsson lennart at augustsson.net
Sat Aug 4 13:44:58 EDT 2007

```Infinity is a very slippery concept, you can't compute with it like that.
You can compute various limits, though.
So, e.g., for a > 0
lim x*a -> Inf
x->Inf
and
lim x*0 -> 0
x->Inf
But
lim x*(1/x) -> 1
x->Inf
And that last one would be "Inf*0" in the limit.  In fact, you can make
Inf*0 any number you like.  So NaN is the sensible.

-- Lennart

On 8/4/07, Andrew Coppin <andrewcoppin at btinternet.com> wrote:
>
>
> >
> >> Um... why would infinity * 0 be NaN? That doesn't make sense...
> > Infinity times anything is Infinity.  Zero times anything is zero.  So
> > what should Infinity * zero be?  There isn't one right answer.  In
> > this case the "morally correct" answer is zero, but in other contexts
> > it might be Infinity or even some finite number other than zero.
>
> I don't follow.
>
> Infinity times any positive quantity gives positive infinity.
> Infinity times any negative quantity gives negative infinity.
> Infinity times zero gives zero.
>
> What's the problem?
>
> > Consider 0.0 / 0.0, which also evaluates to NaN.
>
> Division by zero is *definitely* undefined. (The equation 0 * k = v has
> no solutions.)
>
> _______________________________________________