I'm more or less familiar with the landau symbols, most specifically in computer science for complexity, however I was wondering if someone could clarify a bit for me. I'll just mention that I know that technically the correct notation is to say $f(n)$ is an element of $O(f(n))$, not $f(n) = O(f(n))$.Loosely, my understanding is this, given$ f(n) = n^2 + 2n +log(n)$ Big O represents the upper magnitude, so it would be correct (according to a past CS tutor), but not very accurate, to say $O(f(n)) = n^3$, but incorrect to say $O(n) = log(n)$, whereas the $(f(n)) $represents the lower bound, so it would be correct, but inaccurate to say $(f(n)) = log(n)$ or (not sure about this one), $(f(n)) = 1$.I know that $(f(n))$ is defined as the intersection of $O(f(n))$ and $(f(n))$, but is it valid to drop off lower orders of magnitude in the case of $(f(n))$? ie. is $(f(n)) = n^2$ correct? If not, what is the correct equality?What I am entirely unsure about is $o(f(n))$ and $(f(n))$. I've seen the mathematical definitions and I know that the only difference between them and $O(f(n))$ and $(f(n)) $respectively is that rather than there exists C, it is for all C, but my understanding of mathematical symbols is (at this stage) embarrassing. If anyone could shed some light on all of the above it'd be appreciated, thanks.
Can someone clarify landau symbols definition please?
asymptotics;landau notation