$$\lim_{x\to\infty} \frac {frac(x)} {x} $$(adsbygoogle = window.adsbygoogle || []).push({});

frac(x) is x minus floor function of x. So if x = 2.5, floor function = 2 and frac(x) = 0.5

Hence frac(x) will always be a number between -1 and 1 but never -1 and 1.

By squeeze theorem,

-1 < frac(x) < 1

-1/x < frac(x)/x < 1/x

0 < frac(x)/x < 0

Does this means that $$\lim_{x\to\infty} \frac {frac(x)} {x} = Undefined? $$

Since it is between 0 but not 0.

However WolframAlpha gives the answer as 0.

Shouldn't it be 0 only if it is $$0 \leqslant frac(x)/x \leqslant 0$$

So did I do something wrong or is WolframAlpha wrong?

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# Limits of frac(x)/x

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