Big O notation of max? I'm coding a few set comparisons and noting their big O's using different algorithms and set implementations. I got to one particular function and I decided that it is $O(max(n,m))$ runtime. Is that the proper way to express this?
The expression $O(\max(n,m))$ is meaningful, and we even have $O(n) + O(m) = O(n+m) = O(\max(n,m))$.