  Based on set theoretic ordering properties, a general formulation for
constructing a pair of convertibility monotones, which are generalizations of
distillable entanglement and entanglement cost, is presented. The new pair of
monotones do not always coincide for pure bipartite infinite dimensional states
under SLOCC (stochastic local operations and classical communications),
demonstrating the existence of SLOCC incomparable pure bipartite states, a new
property of entanglement in infinite dimensional systems, with no counterpart
in the corresponding finite dimensional systems.
