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