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Interval Arithmetic

Interval[{min,max}]the interval from min to max
Interval[{min1,max1},{min2,max2},...]
the union of intervals from min1 to max1, min2 to max2, ...

Representations of real intervals.

This represents all numbers between -2 and +5.
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The square of any number between -2 and +5 is always between 0 and 25.
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Taking the reciprocal gives two distinct intervals.
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Abs folds the intervals back together again.
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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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IntervalUnion[interval1,interval2,...]
find the union of several intervals
IntervalIntersection[interval1,interval2,...]
find the intersection of several intervals
IntervalMemberQ[interval,x]test whether the point x lies within an interval
IntervalMemberQ[interval1,interval2]
test whether interval2 lies completely within interval1

Operations on intervals.

This finds the overlap of the two intervals.
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You can use Max and Min to find the end points of intervals.
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This finds out which of a list of intervals contains the point 7.
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You can use intervals not only with exact quantities but also with approximate numbers. Even with machine-precision numbers, Mathematica always tries to do rounding in such a way as to preserve the validity of results.
This shows explicitly the interval treated by Mathematica as the machine-precision number 0.
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This shows the corresponding interval around 100., shifted back to zero.
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The same kind of thing works with numbers of any precision.
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With ordinary machine-precision arithmetic, this computation gives an incorrect result.
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The interval generated here, however, includes the correct value of 0.
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