# Why is this youtuber applying comparing two functions with O(n^2), by applying a contant to one of the functions?

Here is the video in question:https://www.youtube.com/watch?v=BpiMRyWoDu0&t=131s

F(n) and g(n) are both equal to each other since they both have a time complexity of n^2

What's the point of applying the constant c to g(n) to make it 2n^2? What is this trying to show us?

Additionally, why does the inequality include 'equal to'? When will 2n^2 ever be equal to n^2 + n + 3?

Further more, why has he written n >= 4? Where did the 4 come from? I understand why he wrote n >= 3 because n(n-1)is the same as n for time complexity purposes, therefore this becomes n >= 3

• "F(n) and g(n) are both equal to each other since they both have a time complexity of n^2" - of course no. Belonging to same set does not imply equality, when there are more then one element. Apr 20 at 20:03

Look up the definition of big-O. It states that $$f=O(g)\iff \exists c>0:\exists n_0\in\mathbb{N}:\forall n>n_0:f(n)\le cg(n)$$