Category:Theta Notation

This category contains results about $\Theta$ notation.
Definitions specific to this category can be found in Definitions/Theta Notation.

Let $g: \N \to \R$ be a real sequence, expressed here as a real-valued function on the set of natural numbers $\N$.

Then $\map \Theta g$ is defined as:

$\map \Theta g = \map \OO g \cap \map \Omega g$

where:

$\map \OO g$ is big-$\OO$ notation

$\map \Omega g$ is big-$\Omega$ notation.

That is:

$\map \Theta g = \set {f: \N \to \R: \exists c_1, c_2 \in \R_{>0}: \exists n_0 \in \N: \forall n > n_0: 0 \le c_1 \cdot \size {\map g n} \le \size {\map f n} \le c_2 \cdot \size {\map g n} }$