# Is $q(n)=1/n$ a negligible function?

By definition - $q(n)$ is a negligible function if for every positive integer $c>0$ there exist an integer $N_c$ such that for all $x>N_c$ :

• $q(n)<1/x^c$

So for the function $1/x$, if we take the positive integer $c=1$ then we need to find some $N_c$ such that for every $x>N_c$:

• $1/x<1/x$

$=>$ Definitely such $N_c$ does not exist then $1/x$ is not a negligible function.

Is that sufficient?

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Why wouldn't it be? –  poncho Nov 22 '13 at 23:26
Related –  rath Nov 23 '13 at 0:01