Sekirov Dictionary

inverse

/ɪnˈvɝs/

noun 13
adjective 6
verb 1
forms 3

noun13

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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.
The result of an inversion
•
The reverse of any procedure or process.
- Uninstalling is the inverse of installation.
•
A ratio etc. in which the antecedents and consequents are switched.
- The inverse of a:b is b:a.
•
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.
•
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.
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.
•
The negative of a given number.
- The additive inverse of x is -x, as x-x=0, as 0 is the additive identity element.
•
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.
•
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.
A morphism which is both a left inverse and a right inverse.
A grammatical number marking that indicates the opposite grammatical number (or numbers) of the default number specification of noun class.
•
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. — 1850

adjective6

Opposite in effect, nature or order.
Reverse, opposite in order.
Inverted; having a position or mode of attachment the reverse of that which is usual.
•
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.
- Multiplication is the inverse operation to division.
•
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.
- A circle inversion maps a given generalized circle to its inverse generalized circle.
Whose every element has an inverse (morphism which is both a left inverse and a right inverse).

verb1

To compute the bearing and distance between two points.

forms

inversed · inversing · inverses

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