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Old June 5 2013, 10:40 PM   #53
Creepy Critter
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Re: Division By Zero

Reeborg wrote: View Post
Belz... wrote: View Post
Captain McBain wrote: View Post
No, I wasn't kidding.

Chensams wrote: View Post
I'm not math wiz but sense when does 49/0 = infinity?
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'H˘pital'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.
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