What does derangement mean?
Derangement is a formal noun describing a thorough disruption of order — a state in which things that should be arranged or functioning normally have been thrown into confusion. It can apply to concrete systems (the derangement of traffic after a blackout), to bodily or mental functions (as in older medical writing about 'nervous derangement'), or, in mathematics, to a specific kind of permutation in which no element remains in its original position. The word carries a weightier, more technical tone than near-synonyms like 'mess' or 'chaos', making it well suited to formal, academic, or journalistic prose. It derives from the verb 'derange', formed from the French 'déranger', ultimately from Latin roots meaning to un-range, or undo the proper ranking, of things. Though its psychiatric sense of insanity has faded from modern clinical use, the related adjective 'deranged' lives on vividly in everyday speech.
A disturbance of normal order, arrangement, or function; a state of disorder.
"The strike caused a serious derangement of rail services nationwide."
Formal register; often used of systems, plans, or functions rather than physical mess.
(Mathematics) A permutation of a set in which no element appears in its original position.
"The number of derangements of four objects is nine."
A precise combinatorial term; also called a complete permutation.
Regular plural; commonly used in mathematics to count distinct derangements of a set.
"Combinatorics students learn to compute derangements using subfactorials."
In mathematics, a 'derangement' is a permutation where no element stays in its original place — so every single thing must be out of order for it to count.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Etymology of derangement
Derangement derives from the verb 'derange', which entered English from French 'déranger' around the late seventeenth century. The French verb combines the prefix 'dé-' (indicating reversal or removal) with 'ranger' (to arrange in a row), from the Germanic-derived Old French 'rangier'. Thus the word's underlying image is of knocking things out of their proper rank or row. Cognates sharing this root include 'range', 'rank', and 'arrange'.
Related word forms
How derangement is actually used
Derangement is a formal word, more common in written than spoken English. In everyday use it suggests serious disruption of systems or arrangements. Its psychiatric sense ('insanity') is now largely historical and appears mostly in older medical texts, though the adjective 'deranged' remains current as a strong informal insult. The mathematical sense is a precise technical term in combinatorics.
Easily confused with derangement
An arrangement is an ordered, organized state of things — the exact opposite of a derangement, though the two words share the same root.