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:

Interval can be used as a geometric region:

Find the interval that the Wolfram Language 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:

Test for points within an Interval:

Apply it to a list of points to test membership:

Construct the Cantor set by starting with a {0,1} interval and remove the middle third of each interval in each step:

Some steps:

Find the length of the region:

Find a formula for the sequence of lengths using FindSequenceFunction:

Use Max and Min to find end points of intervals:

CenteredInterval represents real intervals or complex rectangles:

Convert a bounded Interval to CenteredInterval representation:

Convert it back:

When interval endpoints are not binary rationals, conversion makes the interval larger:

Intervals are always assumed independent:

A single real variable over the same range yields an interval with a different lower limit: