The Wolfram Language automatically uses sophisticated algorithms to track the precision of approximate numbers. Particularly for some verification applications, however, it is convenient to maintain explicit numerical intervals. All the Wolfram Language's basic mathematical functions and operations automatically operate on Interval objects.

Interval — represent a real interval given by endpoints for arithmetic operations

CenteredInterval — represent a real or complex interval given center and radius

IntervalMemberQ — test whether a number lies within an interval

IntervalUnion — combine intervals together

IntervalIntersection — find common parts of intervals

MinMax — give a list of the min, max values in an interval

RootIntervals — give lists of isolating intervals for polynomial roots

Geometry of Intervals

Region — turn an interval into a geometric region

ArcLength  ▪  RegionMember  ▪  ...

Date & Time Intervals

DateInterval — represent an interval of time

DateBounds  ▪  DateWithinQ  ▪  DateOverlapsQ  ▪  MinDate  ▪  MaxDate