The concept of exchange symmetry is derived from a fundamental postulate of quantum statistics, which states that no observable physical quantity should change after exchanging two identical particles. It states that because all observables are proportional to | ψ ψ | 2 for a system of identical particles, the wave function ψ ψ must either remain the same or change sign upon such an exchange. More generally, for a system of n identical particles the wave function ψ ψ must transform as an irreducible representation of the finite symmetric group S n. It turns out that, according to the spin-statistics theorem, fermion states transform as the antisymmetric irreducible representation of S n and boson states as the symmetric irreducible representation.