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@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.)
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