Dense Sets

Definition

Consider a metric space. A subset of the base set is dense in the base set if every element of the base set is the limit of elements in the subset.

Notation

Let $(A, d)$ be a metric space. Let $B \subset A$. Then $B$ is dense in $A$ if for each $a \in A$ there exists $\seq{b}$ in $B$ so that $\seqt{b} \to a$.