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