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Division by $0$

I was solving a question for my brother today when i got this doubt, i

I arrived at the answer as $\frac{-1}{0}$

Will the answer be infinity since any finite number divided by zero is infinity or should i write it as - $\frac{-1}{0}$ = - infinity ?

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marked as duplicate by Matt N., Listing, David Mitra, Asaf Karagila, Zhen Lin Dec 31 '11 at 15:47

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It is neither -- division by zero is undefined (it is not "infinity" because infinity is a concept, not a number). So you don't have an answer, but you possibly have an argument that there is no answer to whatever the original question is. –  Henning Makholm Dec 31 '11 at 15:27
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An argument that involves division by $0$ is never correct, though the intuitive idea behind it can often be turned into a correct argument. You would need to supply the actual problem to get more detail. –  André Nicolas Dec 31 '11 at 15:28
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I think he means limits of the form $\frac{-1}{0}$. –  Listing Dec 31 '11 at 15:34
    
Once I had a similar confusion: math.stackexchange.com/questions/64456/how-to-define-infty –  gaurav Dec 31 '11 at 17:41
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1 Answer

up vote 2 down vote accepted

The expression is not well defined, consider for example

$$\lim_{x \rightarrow \infty}\frac{-1}{\frac{1}{x}}=-\infty$$

whereas

$$\lim_{x \rightarrow \infty}\frac{-1}{\frac{1}{-x}}=+\infty$$

Both expressions have the form $\frac{-1}{0}$. You have to know how the lower sequence approaches 0, it can even be that the limit does not exist.

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