inverse

1. 1

   Opposite in effect, nature or order.not-comparable

2. 2

   Reverse, opposite in order.not-comparable

3. 3

   Inverted; having a position or mode of attachment the reverse of that which is usual.not-comparable

4. 4

   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.not-comparable

   • Multiplication is the inverse operation to division.
5. 5

   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.not-comparable

   • A circle inversion maps a given generalized circle to its inverse generalized circle.
6. 6

   Whose every element has an inverse (morphism which is both a left inverse and a right inverse).not-comparable

1. 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. 2

   The result of an inversion; The reverse of any procedure or process.

   • Uninstalling is the inverse of installation.
3. 3

   The result of an inversion; A ratio etc. in which the antecedents and consequents are switched.

   • The inverse of a:b is b:a.
4. 4

   The result of an inversion; 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. 5

   The result of an inversion; 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, ¬ mathsf p→¬ mathsf q is the inverse of mathsf p→ mathsf q and is equivalent to the converse proposition mathsf q→ mathsf p.
6. 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. 7

   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:; 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. 8

   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:; 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. 9

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

10. 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.

    • 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.
    • 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.

syn. additive inverse · multiplicative inverse · compositional inverse · inverse point · inverse curve

1. 1

   To compute the bearing and distance between two points.

ant. compute