# inverse

## Definitions

### from The American Heritage® Dictionary of the English Language, 4th Edition

• adj. Reversed in order, nature, or effect.
• adj. Mathematics Of or relating to an inverse or an inverse function.
• adj. Archaic Turned upside down; inverted.
• n. Something that is opposite, as in sequence or character; the reverse.
• n. Mathematics One of a pair of elements in a set whose result under the operation of the set is the identity element, especially:
• n. Mathematics The reciprocal of a designated quantity. Also called multiplicative inverse.
• n. Mathematics The negative of a designated quantity. Also called additive inverse.

• adj. Opposite in effect or nature or order
• adj. reverse, opposite in or order
• adj. Having the properties of an inverse.
• adj. A grammatical number marking that indicates the opposite grammatical number (or numbers) of the default number specification of noun class.
• n. The opposite of a given, due to contrary nature or effect.
• n. The reverse version of a procedure.
• n. The inverse of an element x with respect to a binary operation is an element that when combined with x yields the appropriate identity element.
• n. A statement constructed from the negatives of the premise and conclusion of some other statement: ~p → ~q is the inverse of p → q.
• v. To compute the bearing and distance between two points.

### from the GNU version of the Collaborative International Dictionary of English

• adj. Opposite in order, relation, or effect; reversed; inverted; reciprocal; -- opposed to direct.
• adj. Inverted; having a position or mode of attachment the reverse of that which is usual.
• adj. Opposite in nature and effect; -- said with reference to any two operations, which, when both are performed in succession upon any quantity, reproduce that quantity. The symbol of an inverse operation is the symbol of the direct operation with -1 as an index. Thus sin-1 x means the arc or angle whose sine is x.
• n. That which is inverse.

### from The Century Dictionary and Cyclopedia

• Turned end for end, or in the opposite direction; having a contrary course or tendency; inverted: opposed to direct.
• In mathematics, opposite in nature and effect: said with reference to any two operations which, when both performed in succession upon the same quantity, leave it unaltered: thus, subtraction is inverse to addition, division to multiplication, extraction of roots to the raising of powers, etc.
• n. An inverted state or condition; a direct opposite; something directly or absolutely contrary to something else: as, the inverse of a proposition.
• In logic, with conclusion as hypothesis and hypothesis as conclusion.
• n. In logic, a proposition made by simply interchanging the hypothesis and conclusion of another, without any restriction.
• n. In mathematics, an inverse point, curve, function, ratio, proportion, etc.
• n. In rouge-et-noir, the triangular space in which bets are placed when wagering that the first card dealt for a color will not be the same color as the one that wins the coup: opposed to couleur. See rouge-et-noir.

• n. something inverted in sequence or character or effect
• adj. opposite in nature or effect or relation to another quantity
• adj. reversed (turned backward) in order or nature or effect

## Etymologies

Middle English, from Latin inversus, past participle of invertere, to invert; see invert.
(American Heritage® Dictionary of the English Language, Fourth Edition)
Recorded since 1440, from Latin inversus, the past participle of invertere 'to invert', itself from in- 'in, on' + vertere 'to turn' (Wiktionary)

## Examples

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