This is a question about big theta notation. So, Θ(g(n)) is the set of functions where Θ(g(n))={f(n): there exists positive constants c_1, c_2, and n_0 such that 0

Question

This is a question about big theta notation. So, Θ(g(n)) is the set of functions where Θ(g(n))={f(n): there exists positive constants c_1, c_2, and n_0 such that 0 <= c_1g(n) <= f(n) <= c_2g(n) for all n >= n_0} Why does this constraint exist? 0 <= c_1g(n) <= f(n) <= c_2g(n) for all n >= n_0 Where do they get the c_1g(n) from?

anonymous · Answer

Theta is a combination of Omega and O.

anonymous · Answer

They basically combined definitions.  The purpose of the $c_1g(n)$ is to ensure that is it $f(n)\in \Omega(g(n))$ as well.