Dual number

In linear algebra, the dual numbers extend the real numbers by adjoining one new element ε with the property ε = 0 (ε is nilpotent). The collection of dual numbers forms a particular two-dimensional commutative unital associative algebra over the real numbers. Every dual number has the form z = a + bε where a and b are uniquely determined real numbers. The dual numbers can also be thought of as the exterior algebra of a one dimensional vector space.