Infinity divided by infinity

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

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

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.