Order of magnitude

A logarithmic distance of base-\(b\) numbers, where

if and only if

\[\begin{align*}
x & < y \cdot b^{\pm n} \\[1ex]
y \cdot b^{-n} < x & < y \cdot b^{+n} \\[1ex]
b^{-n} < \frac{x}{y} & < b^{+n}.
\end{align*}
\]

• Practice implementation