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Possible Duplicate:
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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    Once I had a similar confusion: http://math.stackexchange.com/questions/64456/how-to-define-infty2011-12-31

1 Answers 1

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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.