I'm just trying to get my understanding of big O down. I know the concept and the basics but I'm a bit confused about what it means to be equal to big O of something.
For example, is $2^{2n} = O(2^{100n})$? From my understanding it is, since $2^{2n}$ is "faster" than $2^{100n}$, and so completes within the time $2^{100n}$. Is this correct? And if this is true, does it mean that $n$ could have any coefficient greater than $2$ (in this case) such that $2^{2n}$ is equal to $O(2^{mn})$, for all $m > 2$?