As we have seen above, sequences are ordered enumerable sets. This is the basis for the deﬁnition of vectors and matrices .
A vector is a ﬁnite sequence of numbers (usually real numbers). For example, in the Cartesian plane, a vector can be viewed as an arrow from the origin to some point (x, y) ∈ R2. Thus, the vector can be denoted simply by (x, y). Thus, in the plane, a vector is a very short sequence of two components only: x and y. In the three-dimensional space, on the other hand, a vector is denoted by a longer sequence of three components: (x, y, z).