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Dividing by infinity

When dividing by infinity you can have different results. It depends on the contents of the numerator.


Real number

You might not expect, but the division


is wrong. For any real number x the result is 0. The result of the divisions

 ,    ,    ,    ,    ,    ,    , ...

will therefore not be a surprise. The result is always 0, and doesn't depend on the value of the numerator.


Imaginary unit

The imaginary unit i has no real value. Therefore we perform a calculation



Infinity is not a number, and has no fixed value, so

and is undefined.


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