A binary number system is any two-component number system of the form
Here denotes the set of real numbers. Binary numbers are added componentwise and are multplied together using the "foil method" together with the identity .
Three very special examples of binary number systems are
given by the following.
In a similiar manner, the dual number
can be identified with the two by two matrix ,
whose square is the zero matrix. Under this identification the arbitrary
is identified with the two by two matrix .
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