different between inverse vs averse

English

Etymology

Recorded since 1440, from Latin inversus, the past participle of invertere (“to invert”), itself from in- (“in, on”) + vertere (“to turn”).

Pronunciation

• (General American) IPA^(key): /?n?v?s/, /??nv?s/

Adjective

inverse (not comparable)

1. Opposite in effect, nature or order.
2. Reverse, opposite in order.
3. (botany) Inverted; having a position or mode of attachment the reverse of that which is usual.
4. (mathematics) Having the properties of an inverse; said with reference to any two operations, which, when both are performed in succession upon any quantity, reproduce that quantity.

5. (geometry) That has the property of being an inverse (the result of a circle inversion of a given point or geometrical figure); that is constructed by circle inversion.

6. (category theory, of a category) Whose every element has an inverse (morphism which is both a left inverse and a right inverse).

Derived terms

• inverse function
• inverse image
• inverse spelling
• inversely
• inverse video

Related terms

• inversion
• inversive
• reverse

Translations

Noun

inverse (plural inverses)

1. An inverted state: a state in which something has been turned (properly) upside down or (loosely) inside out or backwards.

   Cowgirl is the inverse of missionary.

   321 is the inverse of 123.

2. The result of an inversion, particularly:
   1. The reverse of any procedure or process.

      Uninstalling is the inverse of installation.

   2. (mathematics) A ratio etc. in which the antecedents and consequents are switched.

      The inverse of a:b is b:a.

   3. (geometry) The result of a circle inversion; the set of all such points; the curve described by such a set.

      The inverse P‘ of a point P is the point on a ray from the center O through P such that OP × OP‘ = r² or the set of all such points.

   4. (logic) The non-truth-preserving proposition constructed by negating both the premise and conclusion of an initially given proposition.

      "Anything that isn't a dog doesn't go to heaven" is the inverse of "All dogs go to heaven." More generally, ${\displaystyle \lnot {\mathsf {p}}\to \lnot {\mathsf {q}}}$ is the inverse of ${\displaystyle {\mathsf {p}}\to {\mathsf {q}}}$ and is equivalent to the converse proposition ${\displaystyle {\mathsf {q}}\to {\mathsf {p}}}$.

      • 1896, James Welton, A Manual of Logic, 2nd ed., Bk iii, Ch. iii, §102:

        Inversion is the inferring, from a given proposition, another proposition whose subject is the contradictory of the subject of the original proposition. The given proposition is called the Invertend, that which is inferred from it is termed the Inverse... The rule for Inversion is: Convert either the Obverted Converse or the Obverted Contrapositive.

3. (mathematics) A second element which negates a first; in a binary operation, the element for which the binary operation—when applied to both it and an initially given element—yields the operation's identity element, specifically:
   1. (addition) The negative of a given number.

      The additive inverse of ${\displaystyle x}$ is ${\displaystyle -x}$, as ${\displaystyle x-x=0}$, as ${\displaystyle 0}$ is the additive identity element.

   2. (multiplication) One divided by a given number.

      The multiplicative inverse of ${\displaystyle x}$ is ${\displaystyle x^{-1}}$, as ${\displaystyle x\times x^{-1}=1}$, as ${\displaystyle 1}$ the multiplicative identity element.

   3. (functions) A second function which, when combined with the initially given function, yields as its output any term inputted into the first function.

      The compositional inverse of a function ${\displaystyle f}$ is ${\displaystyle f^{-1}}$, as ${\displaystyle f\ f^{-1}={\mathit {I}}}$, as ${\displaystyle {\mathit {I}}}$ is the identity function. That is, ${\displaystyle \forall x,f(f^{-1}(x))={\mathit {I}}(x)=x}$.

4. (category theory) A morphism which is both a left inverse and a right inverse.
5. (card games) The winning of the coup in a game of rouge et noir by a card of a color different from that first dealt; the area of the table reserved for bets upon such an outcome.
   • 1850, Henry George Bohn, The Hand-book of Games, p. 343:

     If the player... be determined to try his luck on the inverse, he must place his money on a yellow circle, or rather a collection of circles, situated at the extremity of the table.

   • 1950, Lawrence Hawkins Dawson, Hoyle's Games Modernized, 20th ed., p. 291:

     The tailleur never mentions the words ‘Black’ or ‘Inverse’, but always says that Red wins or Red loses, and that the colour wins or the colour loses.

6. (linguistics, Kiowa-Tanoan) A grammatical number marking that indicates the opposite grammatical number (or numbers) of the default number specification of noun class.

Synonyms

• (addition): additive inverse
• (multiplication): multiplicative inverse
• (composition): compositional inverse
• (geometry): inverse point, inverse curve

Translations

See also

• (logic): obverse, converse, contraposition

Verb

inverse (third-person singular simple present inverses, present participle inversing, simple past and past participle inversed)

1. (surveying) To compute the bearing and distance between two points.

Antonyms

• compute (a point).

Anagrams

• Severin, enviers, inserve, veiners, venires, versine

Danish

Adjective

inverse

1. plural and definite singular attributive of invers

Dutch

Pronunciation

• Hyphenation: in?ver?se

Noun

inverse m or f (plural inversen)

1. inverse

Adjective

inverse

1. Inflected form of invers

Anagrams

• viseren

French

Pronunciation

• IPA^(key): /??.v??s/

Etymology 1

From Latin inversus.

Adjective

inverse (plural inverses)

1. inverse, the other way round

Derived terms

• barre inverse

• inversement

Noun

inverse m (plural inverses)

1. the inverse, the contrary

   Synonyms: contraire, envers

Derived terms

Etymology 2

Verb

inverse

1. first-person singular present indicative of inverser
2. third-person singular present indicative of inverser
3. first-person singular present subjunctive of inverser
4. third-person singular present subjunctive of inverser
5. second-person singular imperative of inverser

Further reading

• “inverse” in Trésor de la langue française informatisé (The Digitized Treasury of the French Language).

Anagrams

• enivres, enivrés
• reviens
• Séverin
• vernies

German

Pronunciation

Adjective

inverse

1. inflection of invers:
   1. strong/mixed nominative/accusative feminine singular
   2. strong nominative/accusative plural
   3. weak nominative all-gender singular
   4. weak accusative feminine/neuter singular

Italian

Adjective

inverse

1. feminine plural of inverso

Anagrams

• svenire

Latin

Participle

inverse

1. vocative masculine singular of inversus

English

Etymology

From Latin aversus, past participle of avertere (“to avert”)

Pronunciation

• (Received Pronunciation) IPA^(key): /??v??(?)s/

Adjective

averse (comparative more averse, superlative most averse)

1. Having a repugnance or opposition of mind.

   Synonyms: disliking, disinclined, fromward, unwilling, reluctant, loath

2. Turned away or backward.

   • The tracks averse a lying notice gave, / And led the searcher backward from the cave.

3. (obsolete) Lying on the opposite side (to or from).
4. (heraldry) Turned so as to show the back, as of a right hand.

Usage notes

• The terms adverse and averse are sometimes confused, though their meanings are somewhat different. Adverse most often refers to things, denoting something that is in opposition to someone's interests — something one might refer to as an adversity or adversary — (adverse winds; an attitude adverse to our ideals). Averse usually refers to people, and implies one has a distaste, disinclination, or aversion toward something (a leader averse to war; an investor averse to risk taking). Averse is most often used with "to" in a construction like "I am averse to…". Adverse shows up less often in this type of construction, describing a person instead of a thing, and should carry a meaning of "actively opposed to" rather than "has an aversion to".
• Averse from is an older form, corresponding to the modern averse to.

Derived terms

Related terms

• avert
• aversion

Translations

Verb

averse (third-person singular simple present averses, present participle aversing, simple past and past participle aversed)

1. (transitive, obsolete, rare) To turn away.

See also

• adverse

Anagrams

• Reaves, Seaver, Varese, as ever, re-save, reaves, resave

French

Pronunciation

• IPA^(key): /a.v??s/

Noun

averse f (plural averses)

1. (of rain) shower, rainshower

Further reading

• “averse” in Trésor de la langue française informatisé (The Digitized Treasury of the French Language).

Anagrams

• avères, avérés

Latin

Adjective

?verse

1. vocative masculine singular of ?versus