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Area Mathematics - Functions / General concepts

IEV ref103-01-12

en
interval
set of real numbers such that, for any pair (x, y) of elements of the set, any real number z between x and y belongs to the set

Note 1 to entry: There are several kinds of intervals:

  • closed interval from a to b: [ a,b]={ xR | axb} MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWaamGadaGadeaabaGaaqaaaOqaamaajmcabaGaamyyai aacYcacaaMe8UaamOyaaGaayzxaiaawUfaaiabg2da9maacmaabaGa amiEaiabgIGioJqabiaa=jfacaaMe8+aaqqaaeaacaaMe8Uaamyyai abgYda8iaadIhacqGH8aapcaWGIbaacaGLhWoaaiaawUhacaGL9baa aaa@4B87@
  • open interval from a to b: ] a,b[={ xR | a<x<b} MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWaamGadaGadeaabaGaaqaaaOqaamaajmcabaGaamyyai aacYcacaaMe8UaamOyaaGaayzxaiaawUfaaiabg2da9maacmaabaGa amiEaiabgIGioJqabiaa=jfacaaMe8+aaqqaaeaacaaMe8Uaamyyai abgYda8iaadIhacqGH8aapcaWGIbaacaGLhWoaaiaawUhacaGL9baa aaa@4B87@
  • half-open intervals: ] a,b]={ xR | a<xb} and [ a,b[={ xR | ax<b}
  • closed unbounded interval up to b or onward from a: ] ,b]={ xR | xb} and [ a,+[={ xR | ax}
  • open unbounded interval up to b or onward from a: ] ,b[={ xR | x<b} and ] a,+[={ xR | a<x}

fr
intervalle, m
ensemble de nombres réels tel que, quel que soit le couple (x, y) d'éléments de l'ensemble, tout nombre réel z compris entre x et y appartient à l'ensemble

Note 1 à l'article: On distingue plusieurs catégories d'intervalles:

  • intervalle fermé de a à b: [ a,b]={ xR | axb} MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWaamGadaGadeaabaGaaqaaaOqaamaajmcabaGaamyyai aacYcacaaMe8UaamOyaaGaayzxaiaawUfaaiabg2da9maacmaabaGa amiEaiabgIGioJqabiaa=jfacaaMe8+aaqqaaeaacaaMe8Uaamyyai abgYda8iaadIhacqGH8aapcaWGIbaacaGLhWoaaiaawUhacaGL9baa aaa@4B87@
  • intervalle ouvert de a à b: ] a,b[={ xR | a<x<b} MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWaamGadaGadeaabaGaaqaaaOqaamaajmcabaGaamyyai aacYcacaaMe8UaamOyaaGaayzxaiaawUfaaiabg2da9maacmaabaGa amiEaiabgIGioJqabiaa=jfacaaMe8+aaqqaaeaacaaMe8Uaamyyai abgYda8iaadIhacqGH8aapcaWGIbaacaGLhWoaaiaawUhacaGL9baa aaa@4B87@
  • intervalles semi-ouverts: ] a,b]={ xR | a<xb} et [ a,b[={ xR | ax<b}
  • intervalle illimité fermé commençant en a ou finissant en b: ] ,b]={ xR | xb} et [ a,+[={ xR | ax}
  • intervalle illimité ouvert commençant en a ou finissant en b: ] ,b[={ xR | x<b} et ] a,+[={ xR | a<x}

ar
فترة

de
Intervall, n

es
Intervalo

it
intervallo

ja
区間

pl
przedział
interwał (stosowany w akustyce)

pt
intervalo

sr
интервал, м јд

sv
intervall

zh
区间

Publication date: 2009-12
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