\begin{definition}[Definition:Number Base/Real Numbers]
Let $x \in \R$ be a real number such that $x \ge 0$.
Let $b \in \N: b \ge 2$.
See the definition of Basis Expansion for how we can express $x$ in the form:
:$x = \sqbrk {s \cdotp d_1 d_2 d_3 \ldots}_b$
Then we express $m$ as for integers, and arrive at:
:$x = \sqbrk {r_m r_{m - 1} \ldots r_2 r_1 r_0 \cdotp d_1 d_2 d_3 \ldots}_b$
or, if the context is clear:
:$r_m r_{m - 1} \ldots r_2 r_1 r_0 \cdotp d_1 d_2 d_3 \ldots_b$
\end{definition}