# Can I say θ(g(n)) is the intersection of Ω(g(n)) and O(g(n))?

Let's say Ω(g(n)) be a set representing the lower bound and O(g(n)) be another set representing the upper bound for some function f(n).

Can I say that θ(g(n)) is the intersection of these two sets?

The only reasoning I could give for it is that:

1. Ω(g(n)) is set of all the functions whose running time is at least cg(n) for some c>0.

2. O(g(n)) is set of all the functions whose running time is at most cg(n) for some c>0.

3. θ(g(n)) is the set of all the functions whose running time is in between c1g(n) and c2g(n) for some c1,c2>0.

which kind of looks like it is the intersection of both the sets.

• What are your doubts? Why do you think your claim is not true? – Discrete lizard Mar 21 '19 at 14:53
• Define $\Theta$ more precisely than "somewhat exactly $cg(n)$ for some $c>0$" and the answer will be immediate. – David Richerby Mar 21 '19 at 15:39
• @DavidRicherby done – rsonx Mar 21 '19 at 15:50
• So doesn't it more than "kind of look like" the intersection? – David Richerby Mar 21 '19 at 15:52