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Interval

  • Interval[ min , max ] represents the range of values between min and max.
  • Interval[ , , , , ... ] represents the union of the ranges to , to , ....
  • You can perform arithmetic and other operations on Interval objects.
  • Example: Interval[ 1, 6 ] + Interval[ 0, 2 ].
  • Min[ interval ] and Max[ interval ] give the end points of an interval.
  • For approximate machine- or arbitrary-precision numbers x, Interval[ x ] yields an interval reflecting the uncertainty in x.
  • In operations on intervals that involve approximate numbers, Mathematica always rounds lower limits down and upper limits up.
  • Interval can be generated by functions such as Limit.
  • Relational operators such as Equal and Less yield explicit True or False results whenever they are given disjoint intervals.
  • See the Mathematica book: Section 3.6.8.
  • See also: Range.

    Further Examples

    You can use Max and Min to find the endpoints of intervals.

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    You can take the union and intersection of the two or more intervals.

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    Using IntervalMemberQ, you can check if an interval is contained in another.

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    You can also check if a point belongs to an interval.

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    You can do interval arithmetic with many functions. For example, this command reflects the fact that the square of any real number between -2 and 5 lies between 0 and 25.

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    Taking the reciprocal gives two distinct intervals.

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    You can use intervals in many kinds of functions.

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    Some functions automatically generate intervals.

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    WIth ordinary machine-precision arithmetic, this gives an incorrect result.

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    The interval generated here, however, correctly includes the point 0.

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    Interval arithmetic is useful in obtaining or proving bounds. Here we define a function , which depends on two parameters . We then show that this function is monotonically nonincreasing in for all values of the parameter.

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