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IEVref:103-01-12ID:
Language:enStatus: Standard
Term: interval
Synonym1:
Synonym2:
Synonym3:
Symbol:
Definition: 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}



Publication date:2009-12
Source:
Replaces:
Internal notes:2017-02-20: Editorial revisions in accordance with the information provided in C00020 (IEV 103) - evaluation. JGO
2017-08-25: Corrected final </ul> tag. LMO
CO remarks:
TC/SC remarks:
VT remarks:
Domain1:
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Domain5: