Concept

Restriction (mathématiques)

In mathematics, the restriction of a function is a new function, denoted or obtained by choosing a smaller domain for the original function The function is then said to extend Let be a function from a set to a set If a set is a subset of then the restriction of to is the function given by for Informally, the restriction of to is the same function as but is only defined on . If the function is thought of as a relation on the Cartesian product then the restriction of to can be represented by its graph where the pairs represent ordered pairs in the graph A function is said to be an of another function if whenever is in the domain of then is also in the domain of and That is, if and A (respectively, , etc.) of a function is an extension of that is also a linear map (respectively, a continuous map, etc.). The restriction of the non-injective function to the domain is the injection The factorial function is the restriction of the gamma function to the positive integers, with the argument shifted by one: Restricting a function to its entire domain gives back the original function, that is, Restricting a function twice is the same as restricting it once, that is, if then The restriction of the identity function on a set to a subset of is just the inclusion map from into The restriction of a continuous function is continuous. Inverse function For a function to have an inverse, it must be one-to-one. If a function is not one-to-one, it may be possible to define a partial inverse of by restricting the domain. For example, the function defined on the whole of is not one-to-one since for any However, the function becomes one-to-one if we restrict to the domain in which case (If we instead restrict to the domain then the inverse is the negative of the square root of ) Alternatively, there is no need to restrict the domain if we allow the inverse to be a multivalued function. Selection (relational algebra) In relational algebra, a selection (sometimes called a restriction to avoid confusion with SQL's use of SELECT) is a unary operation written as or where: and are attribute names, is a binary operation in the set is a value constant, is a relation.

À propos de ce résultat
Cette page est générée automatiquement et peut contenir des informations qui ne sont pas correctes, complètes, à jour ou pertinentes par rapport à votre recherche. Il en va de même pour toutes les autres pages de ce site. Veillez à vérifier les informations auprès des sources officielles de l'EPFL.

Graph Chatbot

Chattez avec Graph Search

Posez n’importe quelle question sur les cours, conférences, exercices, recherches, actualités, etc. de l’EPFL ou essayez les exemples de questions ci-dessous.

AVERTISSEMENT : Le chatbot Graph n'est pas programmé pour fournir des réponses explicites ou catégoriques à vos questions. Il transforme plutôt vos questions en demandes API qui sont distribuées aux différents services informatiques officiellement administrés par l'EPFL. Son but est uniquement de collecter et de recommander des références pertinentes à des contenus que vous pouvez explorer pour vous aider à répondre à vos questions.