Size extensivity, introduced by Bartlett, is a more mathematically formal characteristic which refers to the correct (linear) scaling of a method with the number of electrons.
This property of size consistency is of particular importance to obtain correctly behaving dissociation curves.
[3] Hartree–Fock (HF), coupled cluster, many-body perturbation theory (to any order), and full configuration interaction (FCI) are size-extensive but not always size-consistent.
Sometimes numerical errors can cause a method that is formally size-consistent to behave in a non-size-consistent manner.
[4] Core extensivity is yet another related property, which extends the requirement to the proper treatment of excited states.