What is precise definition Little-o ? My definition :
let $f :A \subseteq \mathbb{R} \to \mathbb{R}$ and $g :B \subseteq \mathbb{R} \to \mathbb{R}$ and also $c$ is an cluster point of $A,B$ and
We say that: $$f(x)=o(g(x)) \ \ \ \ \text{as} \ \ \ x \to c$$ if for any $ε > 0$ there exists a neighborhood $U_{\epsilon}$ of $c$ such that $$|f(x)| \leq \epsilon |g(x)| \ \ : \forall x \in ( A \cap B \cap U_{\epsilon} )$$ Is It precise definition ?