A subset $A\subset X$ of a topological space is dense if $$\text{cl}(A)=X.$$

Let $B$ be a Metric Space, and let $A\subset B$. $A$ is dense in $B$ if: $$\forall a\in A, \,\epsilon>0,\,\exists b\in B:\lVert a-b \rVert \le \epsilon$$ ## Intuition An analogous way of stating this is saying that there exist sequences $(a_{n})_{n\in\mathbb{N}}\subset A$ s.t. $\lim_{ n \to \infty }a_{n}\in B$.