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