I do not have much experience in mathematics but I would really like to grasp Big-O notation on its mathematical level. I already read What does the "big O complexity" of a function mean? from references, but I still do not understand (even graphically), what does it mean when we say:
T(n) = O(f(n)) if and only if there are constants c and g such that: T(n) <= c*f(n), where n>=g
Specifically, we say that
T(n) is upper bounded by
c*f(n). What does that actually mean and why does it matter? Does it have to do with eliminating constant factors and low-ordered terms?
Sorry if question is kind of confusing, and thanks for the help!