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What's the difference between $O(1)$ and $o(1)$ ?
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 $o(1)$.
Required, but never shown