Definition:Real Number/Digit Sequence

Definition
Let $b \in \N_{>1}$ be a given natural number which is greater than $1$.

The set of real numbers can be expressed as the set of all sequences of digits:


 * $z = \sqbrk {a_n a_{n - 1} \dotsm a_2 a_1 a_0 \cdotp d_1 d_2 \dotsm d_{m - 1} d_m d_{m + 1} \dotsm}$

such that:
 * $0 \le a_j < b$ and $0 \le d_k < b$ for all $j$ and $k$
 * $\displaystyle z = \sum_{0 \mathop \le j \le n} a_j b^j + \sum_{k \mathop \ge 1} d_k b^{-k}$

It is usual for $b$ to be $10$.

Also see

 * Basis Representation Theorem