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In a lecture, I have seen the following:

Negligible Function: a function $f(n)$ is negligible if $\forall$ polyn. $p \;\exists n_0 \text{ s.t. }\forall n>n_o\; f(n) < 1/p(n)$

  • What is exactly $n_0$? Why is there an $n_0$ in the definition?
  • Why does not it suffice to say $\forall n, f(n) < 1/p(n)$ ?
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marked as duplicate by graphtheory92, Gilles 'SO- stop being evil', kelalaka, kodlu, Maarten Bodewes Jan 7 at 16:28

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