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Interval arithmetic is a mathematical technique used to put bounds on rounding errors and measurement errors in mathematical computation. Numerical methods using interval arithmetic can guarantee reliable and mathematically correct results. Instead of representing a value as a single number, interval arithmetic represents each value as a range of possibilities. For example, instead of saying the height of someone is approximately 2 meters, one could, using interval arithmetic, say that the height of the person is definitely between 1.97 meters and 2.03 meters.
Mathematically, using interval arithmetic, instead of working with an uncertain real-valued variable x {\displaystyle x} , one works with an interval {\displaystyle } that defines the range of values that x {\displaystyle x} can have. In other words, any value of the variable x {\displaystyle x} lies in the closed interval between a {\displaystyle a} and b {\displaystyle b}. A function f {\displaystyle f} , when applied to x {\displaystyle x} , yields an inexact value; f {\displaystyle f} instead produces an interval {\displaystyle } which includes all the possible values for f {\displaystyle f} for all x ∈ {\displaystyle x\in }.