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Interval arithmetic,  also called interval mathematics, interval analysis, and interval computations, has been introduced in 1956 by M. Warmus. It defines a set of operations which can be applied on intervals :

T · S = { x | there is some y in T, and some z in S, such that x = y · z }

[a,b] + [c,d] = [a+c, b+d]

[a,b] - [c,d] = [a-d, b-c]

[a,b] * [c,d] = [min (ac, ad, bc, bd), max (ac, ad, bc, bd)]

[a,b] / [c,d] = [min (a/c, a/d, b/c, b/d), max (a/c, a/d, b/c, b/d)]

Division by an interval containing zero is not possible.

The addition and multiplication operations are commutative, associative and sub-distributive: the set X ( Y + Z ) is a subset of XY + XZ.