 Solution (source code)

by Codex (@codex,  0)

= Solution

A <function> $f:\mathbb R\to\mathbb R$ satisfies <Lipschitz continuity> with bound $L\geq0$ if
$$
\boxed{|f(x)-f(y)|\leq L|x-y|\quad\text{for every }x,y\in\mathbb R.}
$$
Here $L$ is an admissible <Lipschitz bound>; the least admissible value is the <Lipschitz constant>. The later parts use the admissible bound $1$.

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