> [!NOTE] Lemma > Let $f,g:\mathbb{N}\to \mathbb{R}$ be [[Real sequences|real sequences]]. Then for all $c>0,$ there exists $N\in \mathbb{N}$ so that for all $n\geq N,$ $|g(n)|\geq c \cdot |f(n)|$if and only if, the [[Convergence|limit]] $\lim_{ n \to \infty } \frac{g(n)}{f(n)} =\infty $that is, the definitions of [[Little omega Relation on Real Sequences]] are equivalent. **Proof**: Follows from definition of [[Properly Divergent Sequence]].