I am trying to figure out some stuff here with Big O Notation. I mean I understand the concept of it and can generally be able to tell what the efficiency of something is, but I do not really understand how to find witnesses. Here is an example of one that I need to do. Can anyone help me understand this? Thanks in advance!
Example 1: $n^2$ is $O(0.001n^3)$.
Example 2: $25n^4 − 19n^3 + 13n^2 − 106n + 77$ is $O(n^4)$.