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Zero divided by infinite

The result of the division

is no surprise.

 


Explanation

The numerator of the fraction is zero, and the denominator is unequal zero. But it also applies to

 ,    , ...

and now you can expect that every real number x gives

However, take care, as infinity is not a number, and so

is undefined. If this division emerges in another way, you will get a solution, as

Here you work with n→∞ and that means: It approaches infinite, but is not infinite. The nominator and the denominator get the the same (infinite) value, and a division is thus allowed.

 


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