Definition:Number Base/Real Numbers
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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:
- $x = \sqbrk {s \cdotp d_1 d_2 d_3 \ldots}_b$
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:
- $r_m r_{m - 1} \ldots r_2 r_1 r_0 \cdotp d_1 d_2 d_3 \ldots_b$
Also see
The most common number base is of course base $10$.
So common is it, that numbers written in base $10$ are written merely by concatenating the digits:
- $r_m r_{m - 1} \ldots r_2 r_1 r_0$
$2$ is a fundamentally important number base in computer science, as is $16$:
- Results about number bases can be found here.
Sources
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): base (for representation of numbers)