Definition 3.1.1 (Dyadic Rational Number). Let $x \in \rational$, then $x$ is a dyadic rational number if there exists $n \in \natp$ and $k \in \nat$ such that $x = k/2^{-n}$.

For each $n \in \natp$, denote $\mathbb{D}_{n} = \bracs{k/2^{-n}|k \in \integer}$. The set $\mathbb{D}= \bigcup_{n \in \natp}\mathbb{D}_{n}$ is the collection of all dyadic rational numbers.