Built-in Mathematica Symbol

Interval

Interval[{min, max}]
represents the range of values between min and max.

Interval[{min₁, max₁}, {min₂, max₂}, ...]
represents the union of the ranges min₁ to max₁, min₂ to max₂, ....

Interval[{min, max}] represents the closed interval that includes both end points.

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:

Indeterminate limits can give intervals:

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 0.:

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: