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
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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