Making sense of asymptotic notation
The easiest way to remember asymptotic notation is to memorize the following table:
$$
\begin{array}{cc}
o &amp; &lt; \\
O &amp; \leq \\
\Theta &amp; = \\
\Omega &amp; \geq \\
\omega &amp; &gt;
\end{array}
$$
For example, if $f(n) = O(g(n))$ then asymptotically and up to a constant multiple, $f(n) \leq g(n)$; formally, there exists a constant $C &gt; 0$ such that $f(n) \leq Cg(n)$ for large enough $n$. In your case, clearly the average case is at most the worst case, and so $A(n) = O(W(n))$.