# Why is O notation the worst case? [duplicate]

I don't understand why O notation is the worst case. If this notations describes a function f such that 0 <= f(n) <= cg(n), we can see that in any case f will be smaller that the original function g that describes the running time. In my idea, f(n) describes a better option because the running time is less for any input n. Someone can explain me please why O notation is the worst case?﻿

It doesn't, if $$f \in O(g)$$, it "just" tells us that $$g$$ is an asypmtotic upper bound for $$f$$.