inverse

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

   The reverse of any procedure or process.

   Uninstalling is the inverse of installation.

3. A ratio etc. in which the antecedents and consequents are switched.

   The inverse of a:b is b:a.

4. 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.

5. The non-truth-preserving proposition constructed by negating both the premise and conclusion of an initially given proposition.

6. 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:

   The negative of a given number.

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

7. One divided by a given number.

   The multiplicative inverse of x is x⁻¹, as x×x⁻¹=1, as 1 the multiplicative identity element.

8. 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 ff⁻¹= mathit I, as mathit I is the identity function. That is, ∀x,f(f⁻¹(x))= mathit I(x)=x.

9. A morphism which is both a left inverse and a right inverse.

10. 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.

11. A grammatical number marking that indicates the opposite grammatical number (or numbers) of the default number specification of noun class.

1. The derivatives of the inverse trigonometric functions are algebraic.

   deDie Ableitungen der inversen trigonometrischen Funktionen sind algebraisch. — quicksanddiver

   CC BY 2.0 FR · Tatoeba · FlamingTofu · C2Open on TatoebaReport a problem

2. The inverse of a non-square matrix is a dangerous thing.

   ruОбратная не квадратной матрицы, это опасная вещь. — FeuDRenais

   deDie Inverse einer nichtquadratischen Matrix ist ein gefährliches Ding. — Yorwba

   CC BY 2.0 FR · Tatoeba · FeuDRenais · C1Open on TatoebaReport a problem

3. Correction. It's the inverse.

   CC BY 2.0 FR · Tatoeba · Eccles17 · C1Open on TatoebaReport a problem

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