Thursday, 2 July 2015

indeterminate forms - I have learned that 1/0 is infinity, why isn't it minus infinity?



My brother was teaching me the basics of mathematics and we had some confusion about the positive and negative behavior of Zero. After reading a few post on this we came to know that it depends on the context of its use.



Why do we take 1/0 as positive infinity rather than negative infinity (we come close to zero from negative axis)?


Answer



The other comments are correct: $\frac{1}{0}$ is undefined. Similarly, the limit of $\frac{1}{x}$ as $x$ approaches $0$ is also undefined. However, if you take the limit of $\frac{1}{x}$ as $x$ approaches zero from the left or from the right, you get negative and positive infinity respectively.


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