Inverse

English

Etymology

Recorded since 1440, from Template:Uder, the past participle of Template:M, itself from Template:M + Template:M.

Pronunciation

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Adjective

A chart depicting the strong inverse relationship between prosperity and fertility in existing societies

1. Opposite in effect, nature or order.
2. Reverse, opposite in order.
3. Template:Lb Inverted; having a position or mode of attachment the reverse of that which is usual.
4. Template:Lb 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.

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5. Template:Lb 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. Template:C

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6. Template:Lb Whose every element has an inverse (morphism which is both a left inverse and a right inverse).

Related terms

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Translations

• Bulgarian: Template:T+
• Catalan: Template:T+
• Chinese:

  Mandarin: Template:T+

• Czech: Template:T
• Dutch: Template:T+, Template:T+
• Finnish: Template:T+
• French: Template:T+
• German: Template:T+
• Spanish: Template:T+

• Azerbaijani: Template:T+
• Bulgarian: Template:T+
• Catalan: Template:T+
• Chinese:

  Mandarin: Template:T+

• Dutch: Template:T+
• Esperanto: Template:T
• Finnish: Template:T+, Template:T+
• French: Template:T+
• German: Template:T+

• Azerbaijani: Template:T+
• Bulgarian: Template:T+
• Catalan: Template:T+
• Chinese:

  Mandarin: Template:T+

• Dutch: Template:T+
• Finnish: Template:T, Template:T+
• Spanish: Template:T+
• Swedish: Template:T+

• Esperanto: Template:T-check
• French: Template:T+check
• Japanese: Template:T+check

Noun

1. An inverted state: a state in which something has been turned Template:Lb upside down or Template:Lb 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. Template:Lb A ratio etc. in which the antecedents and consequents are switched.

      The inverse of a:b is b:a.

   3. Template:Lb 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. Template:Lb 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, $\mathrm{\neg }𝗉\to \mathrm{\neg }𝗊$ is the inverse of $𝗉\to 𝗊$ and is equivalent to the converse proposition $𝗊\to 𝗉$.

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3. Template:Lb 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. Template:Lb The negative of a given number.

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

   2. Template:Lb One divided by a given number.

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

   3. Template:Lb 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 $f$ is $f^{-1}$, as $f{f}^{-1}=𝐼$, as $𝐼$ is the identity function. That is, $\mathrm{\forall }x,f(f^{-1}(x))=𝐼(x)=x$.

4. Template:Lb A morphism which is both a left inverse and a right inverse.
5. Template:Lb 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.
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6. Template:Lb A grammatical number marking that indicates the opposite grammatical number (or numbers) of the default number specification of noun class.

Synonyms

• Template:Sense Template:L inverse
• Template:Sense Template:L inverse
• Template:Sense Template:L inverse
• Template:Sense inverse Template:L, inverse Template:L

Translations

• Bulgarian: Template:T+
• Dutch: Template:T+, Template:T+, Template:T+
• Finnish: Template:T+

• Bulgarian: Template:T+
• Dutch: Template:T+, Template:T+
• Finnish: Template:T
• Trió: Template:T

• Bulgarian: Template:T
• Chinese:

  Mandarin: Template:T+

• Dutch: Template:T+
• Finnish: Template:T+
• Hindi: Template:T+

• Chinese:

  Mandarin: Template:T

• Finnish: Template:T, Template:T
• Korean: Template:T+

• French: Template:T+check, Template:T+check
• Japanese: Template:T+check
• Swedish: Template:T+check

See also

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Verb

1. Template:Lb To compute the bearing and distance between two points.

Antonyms

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Anagrams

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Danish

Adjective

1. Template:Da-e-form of

Dutch

Pronunciation

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Noun

1. Template:L

Adjective

1. Template:Infl of

Anagrams

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French

Pronunciation

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Etymology 1

From Template:Der.

Adjective

1. Template:L, the other way round

Derived terms

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Noun

1. the Template:L, the contrary

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Etymology 2

Verb

1. Template:Inflection of

Further reading

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Anagrams

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German

Pronunciation

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Adjective

1. Template:De-adj form of

Italian

Adjective

1. Template:Feminine plural of

Anagrams

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Latin

Participle

1. Template:Inflection of