non-decreasing function

noun

UK /nɒn dɪˈkriːsɪŋ ˈfʌŋkʃən/

US /nɑːn dɪˈkriːsɪŋ ˈfʌŋkʃən/

A function that never goes down as you move along the x-axis.

The sequence 1, 2, 2, 5, 5, 9 is non-decreasing because each number is at least as big as the one before it.

SYNONYMS

monotone non-decreasing function order-preserving function isotone function weakly increasing function

RELATED WORDS

monotonic function increasing function step function cumulative distribution function order theory

OTHER MEANINGS

2. A function f such that x ≤ y implies f(x) ≤ f(y) for all x and y in its domain.

Every constant function is non-decreasing, since equal inputs give equal outputs.

3. A real-valued function whose graph never slopes downward from left to right.

The graph of a non-decreasing function may be flat in places but never falls.

4. A sequence a₁, a₂, … with aₙ ≤ aₙ₊₁ for every index n.

The running maximum of a list forms a non-decreasing sequence.