doubt in asymptotic notation

Question

given : 1/4 and 1

 

1/4 = theta(1)

is this correct

or only this 1/4 = O(1)

Answer 1

The definition of $\Theta$ goes like this: $f(n) = \Theta(g(n)) \implies c_1g(n)\le f(n) \le c_2g(n) \,(\exists n_0 \forall n\gt n_0 ,c_1,c_2\gt0)$.

Here, $\frac{1}{4} \le 1$ and $\frac{1}{4} \ge \frac{1}{5}*1$. Hence the $\Theta$ definition fits.