= Nonincreasing function
{title2=$x<y\implies f(x)\geq f(y)$}
= Nonincreasing
{synonym}
A <real-valued function> $f:D\to\mathbb R$ is a <nonincreasing function> if every pair $x<y$ in its <domain of a function> satisfies $f(x)\geq f(y)$. Equal outputs and flat <intervals> are allowed. For example, $f(x)=-\min(1,\max(0,x))$ is a <nonincreasing function>, with a falling segment between two flat portions. Requiring $f(x)>f(y)$ instead gives a <strictly decreasing function>. Negating a <nondecreasing function> gives a <nonincreasing function>.
A <nonincreasing> <sequence> of <natural numbers> has finitely many strict drops, so it is eventually constant. This differs from a <strictly decreasing> <sequence>, which cannot continue indefinitely within the <natural numbers>.
// Target: foundations-of-mathematics.bigb
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