To illustrate, suppose we have a system of N bosons that occupy mutually orthogonal single-particle states | ϕ ϕ 1 ⟩ ⟩ , | ϕ ϕ 2 ⟩ ⟩ , | ϕ ϕ 3 ⟩ ⟩ , etc. Using the usual representation, we demonstrate the system by assigning a state to each particle and then imposing exchange symmetry.