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 and :
 In:= Out= The square of any number between and is always between and :
 In:= Out= Taking the reciprocal gives two distinct intervals:
 In:= Out= Abs folds the intervals back together again:
 In:= Out= You can use intervals in many kinds of functions:
 In:= Out= Some functions automatically generate intervals:
 In:= Out= 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:
 In:= Out= You can use Max and Min to find the end points of intervals:
 In:= Out= This finds out which of a list of intervals contains the point 7:
 In:= Out= You can use intervals not only with exact quantities but also with approximate numbers. Even with machineprecision numbers, the Wolfram Language always tries to do rounding in such a way as to preserve the validity of results.

This shows explicitly the interval treated by the Wolfram Language as the machineprecision number 0.
 In:= Out= This shows the corresponding interval around 100., shifted back to zero:
 In:= Out= The same kind of thing works with numbers of any precision:
 In:= Out= With ordinary machineprecision arithmetic, this computation gives an incorrect result:
 In:= Out= The interval generated here, however, includes the correct value of 0:
 In:= Out= 