of arbitrary, but finite, length formula_33 and for which formula_34 are scalars and formula_35 are members of formula_31. Intuitively, this is a linear combination of the basis vectors in the usual sense of expanding an element of a vector space. We call this a "formal expression" because technically it is illegal to multiply formula_37 since there is no defined multiplication operation by default on an arbitrary set and arbitrary field of scalars. Instead, we will "pretend" (similar to defining the imaginary numbers) that this refers to something, and then will go about manipulating it according to the rules we expect for a vector space, e.g. the sum of two such strings using the same sequence of members of formula_31 is