Definition:Number Base/Real Numbers

Definition
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:


 * $x = \left[{s \cdotp d_1 d_2 d_3 \ldots}\right]_b$

Then we express $m$ as for integers, and arrive at:
 * $x = \left[{r_m r_{m-1} \ldots r_2 r_1 r_0 \cdotp d_1 d_2 d_3 \ldots}\right]_b$

or, if the context is clear:
 * $r_m r_{m-1} \ldots r_2 r_1 r_0 \cdotp d_1 d_2 d_3 \ldots_b$