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