= Lipschitz bound
{c}
{title2=$d_Y(f(x),f(y))\leq Ld_X(x,y)$}
A Lipschitz bound is any valid inequality of the displayed form with a finite constant $L$. It need not use the least <Lipschitz constant>. For $f(x)=3x-2$, both $L=3$ and $L=5$ are valid, but $L=2$ fails. The tighter bound gives a sharper error estimate: input error at most $0.01$ guarantees output error at most $0.03$ using $L=3$, compared with the valid but weaker $0.05$ using $L=5$. The bound constrains errors; it does not state that every pair achieves that amplification.
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