monotone function

Fetched 2026-10-26 (cache).

Synonyms: monotonic function

Antonyms: monotonic function

Related words from Datamuse; suggestions, not definitions.

Noun

1. {{lb|en|calculus}} A [[function]] ''f'' : ''X''→'''R''' (where ''X'' is a [[subset]] of '''R''', possibly a [[discrete set]]) that either never decreases or never increases as its [[independent variable]] increases; that is, either ''x'' ≤ ''y'' implies ''f''(''x'') ≤ ''f''(''y'') or ''x'' ≤ ''y'' implies ''f''(''y'') ≤ ''f''(''x''). {{C|en|Functions}}
2. {{lb|en|order theory|analysis}} A function ''f'' : ''X''→''Y'' (where ''X'' and ''Y'' are [[poset]]s with [[partial order]] "≤") with either: (1) the property that ''x'' ≤ ''y'' implies ''f''(''x'') ≤ ''f''(''y''), or (2) the property that ''x'' ≤ ''y'' implies ''f''(''y'') ≤ ''f''(''x'').
3. {{lb|en|Boolean algebra}} A [[Boolean function]] with the property that switching any one input variable from 0 to 1 results either in no change in output or a change from 0 to 1.

Source: Wiktionary · CC BY-SA 4.0 (Wiktionary dump) · cached copy, not a rewrite.