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

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

• See this. – Mooncrater Sep 28 '17 at 6:00
• I know the definition:-) – mallea Sep 28 '17 at 13:01
• Then what's the question? The two are different sets, one being a (proper) subset of the other. – 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 $o(1)$.