A mapping is an isomorphism if is a homomorphism from to , and is a homomorphism from to .
Addition inherits the identity while multiplication inherits the identity .
Since intervals were constructed with mathematical rigor in mind, several nice properties are obeyed by intervals. The above property can be extended by considering that interval addition is commutative. In general, a real computation result is guaranteed to be contained in the result of the associated interval computation because the interval inclusion property is transitive.