Thread: Division By Zero View Single Post
June 6 2013, 11:19 PM   #56
CorporalCaptain

Location: North America
Re: Division By Zero

CorporalCaptain wrote:
Reeborg wrote:
 Belz... wrote: No, because infinity times zero is still zero.
I doubt that. In fact: Infinity*Zero = undefined/not solvable but NOT Zero. Lim (X-> INF) X * (1/X) = INF * ZERO = ONE but Lim (X-> INF) (2*X) * (1/X) = INF * ZERO = TWO. Conclusion there is NO (exact) solution to Infinity*Zero; and most certainly it's not = ZERO.
Actually, also, in your notation, Lim (X-> INF) X * exp(-X) = INF * ZERO = ZERO.

Proof, by l'Hôpital's rule: Lim (X-> INF) X * exp(-X) = Lim (X-> INF) X / exp(X) = Lim (X-> INF) 1 / exp(X) = Lim (X-> INF) exp(-X) = ZERO. QED.

INF * ZERO is one of the indeterminate forms.
Just to round things out, I should also point out that one can have, as it were, INF * ZERO = INF.

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