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based on an earlier version of the Wolfram Language.
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Interval

Interval
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.
  • Interval represents the closed interval that includes both end points.
  • 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.
  • Relational operators such as Equal and Less yield explicit True or False results whenever they are given disjoint intervals.
Add intervals, getting an interval representing the result:
Indeterminate limits can give intervals:
Add intervals, getting an interval representing the result:
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Indeterminate limits can give intervals:
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Squaring gives a non-negative interval:
Some functions can be applied to an interval:
Exact inputs yield exact interval results:
Disjoint intervals can be generated:
Exact comparisons can be made with intervals:
Solve an equation involving an interval:
Approximate numbers automatically turn into intervals:
Machine numbers always correspond to a certain interval:
Find the interval that Mathematica considers consistent with machine number :
Specifying a different precision gives a different interval:
Watch the widening of intervals in a system with sensitive dependence on initial conditions:
With machine-precision evaluation, this gives a definite but incorrect value:
With Interval, the result spans the correct value:
Show how the bounds of an interval vary with a parameter:
Use Max and Min to find end points of intervals:
Intervals are always assumed independent:
A single real variable over the same range yields an interval with a different lower limit:
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