How does asymptotic notation work?

Question

I just don’t understand the f(n) = O(n) if f(n) <= C * N for N >= N_0. Also how is this relevant to runtime?

In: 0

Answer 1

Something I want to add to the other answer, since I always found the equal sign disturbing:
*O(n)* is a set and NOT really equal to *f(n)*. So the commonly used notation *f(n) = O(n)* actually means *f(n) is in O(n).*

What you have written there means: *f(n) is in the set called O(n) if the following property holds: …*