What's the difference between $O(1)$ and $o(1)$ ?

  • $\begingroup$ See this. $\endgroup$ – Mooncrater Sep 28 '17 at 6:00
  • $\begingroup$ I know the definition:-) $\endgroup$ – mallea Sep 28 '17 at 13:01
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    $\begingroup$ Then what's the question? The two are different sets, one being a (proper) subset of the other. $\endgroup$ – Raphael Sep 28 '17 at 14:06

A function is $O(1)$ if it is bounded from above. It is $o(1)$ if it tends to zero. Any function which is $o(1)$ is also $O(1)$.

For example, $\sin^2 x$ is $O(1)$ but not $o(1)$, and $1/x$ is both $O(1)$ and $o(1)$.

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