> [!NOTE] Definition > Let $f,g: \mathbb{N}\to \mathbb{R}$ be [[Real sequences|real sequences]]. Then $g(n)$ is big Omega of $f(n),$ denoted $g(n)=\Omega (f(n)),$ iff there exists $c>0,$ $N\in \mathbb{N}$ so that for all $n \geq N,$ $|g(n)|\geq c \cdot |f(n)|$ # Properties By [[Big Omega is Inverse Relation of Big O on Real Sequences]], $g(n)=\Omega(f(n))$ iff $f(n)=\mathcal{O}(g(n))$, that is $f(n)$ is [[Big O Relation on Real Sequences|big O]] of $g(n),$ thus it is sufficient to study $\mathcal{O}(f(n))$ and its properties.