Given a bipartite quantum system represented by a Hilbert space H₁⊗H₂, we give an elementary argument to show that if either dim H₁ = ∞ or dim H₂ = ∞, then the set of nonseparable density operators on H₁⊗H₂ is trace-norm dense in the set of all density operators (and the separable density operators nowhere dense). This result complements recent detailed investigations of separability, which show that when dim H_i<∝ for i = 1,2, there is a separable neighborhood (perhaps very small for large dimensions) of the maximally mixed state.