# Definitions Let $f,g$ be [[Real sequences|real sequences]]. > [!NOTE] Definition 1 > $g$ is little omega of $f,$ denoted $g=\omega(f),$ if and only if for all $c>0,$ there exists $N\in \mathbb{N}$ so that for all $n\geq N,$ $|g(n)|\geq c \cdot |f(n)|$ > [!NOTE] Definition 2 > Equivalently, $g=\omega(f),$ iff the [[Convergence|limit]] $\lim_{ n \to \infty } \frac{g(n)}{f(n)} =\infty $ **Note**: By [[Equivalence of Definitions of Little omega Relation on Real Sequences]], the above definitions are indeed equivalent. # Properties By [[Little omega Relation on Real Sequences is Strict Order Relation]], ... By [[Little omega Relation on Real Sequences equals not Big O]], ...