# Associations to the word «Inverse»

## Wiktionary

INVERSE, adjective. Opposite in effect or nature or order
INVERSE, adjective. Reverse, opposite in order
INVERSE, adjective. (botany) Inverted; having a position or mode of attachment the reverse of that which is usual.
INVERSE, adjective. (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.
INVERSE, adjective. (linguistics) (Kiowa-Tanoan) A grammatical number marking that indicates the opposite grammatical number (or numbers) of the default number specification of noun class.
INVERSE, adjective. (category theory) A morphism which is both a left inverse and a right inverse.
INVERSE, noun. The opposite of a given, due to contrary nature or effect.
INVERSE, noun. The reverse version of a procedure.
INVERSE, noun. (mathematics) The inverse of an element x with respect to a binary operation is an element that when combined with x yields the appropriate identity element.
INVERSE, noun. (logic) A statement constructed from the negatives of the premise and conclusion of some other statement: ~p → ~q is the inverse of p → q.
INVERSE, verb. (surveying) To compute the bearing and distance between two points.
INVERSE CONDEMNATION, noun. (legal) The taking of private property by the government without providing compensation, thus forcing the previous owner to file a lawsuit against the government to recover the value of the property taken.
INVERSE COSINE, noun. Arccosine
INVERSE FOURIER TRANSFORM, noun. (mathematics) A mathematical operation that transforms a function for a discrete or continuous spectrum into a function for the amplitude with the given spectrum; an inverse transform of the Fourier transform.
INVERSE FOURIER TRANSFORMS, noun. Plural of inverse Fourier transform
INVERSE FUNCTION, noun. (mathematics) A function that does exactly the opposite of another; formally g is the inverse function of a function f if and only if: $$\forall x . f(x) = y \implies g(y) = x$$. Notation: $$f^{-1}$$.
INVERSE FUNCTIONS, noun. Plural of inverse function
INVERSE HYPERBOLIC FUNCTION, noun. The inverse of a hyperbolic function
INVERSE HYPERBOLIC FUNCTIONS, noun. Plural of inverse hyperbolic function
INVERSE IMAGE, noun. The set of points that map to a given point (or set of points) under a specified function.
INVERSE IMAGES, noun. Plural of inverse image
INVERSE LIMIT, noun. (algebra) A subset of the Cartesian product of all the groups of an inverse system, which subset is determined by the following criteria: (1) that, given that each element of the subset is itself a directed poset of "projected" group elements, that if any two such projected group elements relate through the ordering relation, then the "smaller" element should be a homomorphic projection of the "larger" element, where the homomorphism is the corresponding one from the inverse system; (2) that the subset be the largest one for which all of its elements satisfy the preceding property.
INVERSE LIMIT, noun. (category theory) The categoretic generalization of the previous definition, where groups become objects, homomorphisms become morphisms, and the second condition becomes the universal property. The Cartesian product becomes the vertex of a particular cone which is the limit.
INVERSE MATRICES, noun. Plural of inverse matrix
INVERSE MATRIX, noun. (linear algebra) Of a matrix A, another matrix B such that A multiplied by B and B multiplied by A both equal the identity matrix.
INVERSE SYSTEM, noun. (algebra) An indexed family of groups whose index set is a directed poset, together with a set of homomorphisms which are indexed by a subset of the Cartesian product of the index set with itself — which subset corresponds to the ordering relation of the directed poset — such that the domain and codomain of each homomorphism is obtained by reversing its ordered pair of indexes $$(e.g., f_{i j} : G_j \rightarrow G_i)$$, and such that the homomorphisms compose in a way which reflects the reflexivity and transitivity of the order relation.
INVERSE SYSTEM, noun. (category theory) A generalization of the above definition, where groups are replaced by objects, and homomorphisms are replaced by morphisms.
INVERSE TRIGONOMETRIC FUNCTION, noun. (mathematics) A function that is the inverse of an appropriate restriction of a trigonometric function.
INVERSE TRIGONOMETRIC FUNCTIONS, noun. Plural of inverse trigonometric function
INVERSE VIDEO, noun. (computing) (dated) A display technique whereby background and foreground colours are interchanged, typically used for highlighting.

## Dictionary definition

INVERSE, noun. Something inverted in sequence or character or effect; "when the direct approach failed he tried the inverse".
INVERSE, adjective. Reversed (turned backward) in order or nature or effect.
INVERSE, adjective. Opposite in nature or effect or relation to another quantity ; "a term is in inverse proportion to another term if it increases (or decreases) as the other decreases (or increases)".

## Wise words

Life has no meaning unless one lives it with a will, at least to the limit of one's will. Virtue, good, evil are nothing but words, unless one takes them apart in order to build something with them; they do not win their true meaning until one knows how to apply them.
Paul Gauguin