Now if we take the shorthand notation of writing the basis vector in L ∞ (A * × A * ) corresponding to a pair of strings as the pair of strings itself thenb = 1 3 (a, cd) + 1 3 (a, fd) (30) It would thus seem sensible to define multiplication of contexts so that 1 3 (a, cd) • 1 3 (ab, d) = 1 3 (a, d).
we then find showing that this definition of multiplication doesn't provide us with what we are looking for.