 Cardinalities of monotone natural-number functions

Nondecreasing functions $\mathbb{N}\to \mathbb{N}$ form an uncountable set: every subset $A$ is encoded by the strictly increasing function $n+{\sum }_{k=1}^n{1}_A(k)$. In contrast, nonincreasing functions form a countable set because each is determined by a finite initial segment and its eventual constant value.

// Target: classical-mechanics.bigb