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Infinity divided by infinity

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

 


Explanation

The calculations of

3 × ∞ = ∞  , 2 × ∞ = ∞  , 1 × ∞ = ∞  , ...

are not really surprising. As a consequence, the results of the fractions

          

are all different, so we find

From this it follows that another solution could be

          

and that means again it applies

 


Limits

You can solve the fraction with L'Hôpital's rule if it concerns limits

The numerator and denominator have the same infinite value in this case. That can be the outcome of a calculation.

 


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