IEVref:103-01-12ID:
Language:enStatus: backup
Term: interval
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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 There are several kinds of intervals:

  • closed interval from a to b: [ a, b]={ x∈R  |  a≤x≤b} 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[={ x∈R  |  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]={ x∈R  |  a<x≤b} and [ a, b[={ x∈R  |  a≤x<b}

  • closed unbounded interval up to b or onward from a: ] −∞, b]={ x∈R  |  x≤b} and [ a, +∞[={ x∈R  |  a≤x}

  • open unbounded interval up to b or onward from a: ] −∞, b[={ x∈R  |  x<b} and ] a, +∞[={ x∈R  |  a<x}



Publication date:2009-12
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