Interval Arithmetic
| Interval[{min,max}] | the interval from min to max |
| Interval[{min1,max1},{min2,max2},...] |
| the union of intervals from  to  ,  to  , ... |
Representations of real intervals.
This represents all numbers between
and
.
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The square of any number between
and
is always between
and
.
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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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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
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This shows the corresponding interval around
, 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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lies completely within 
