We examine the role of the Zeeman interaction in determining the bound states of the trion at magnetic fields up to 50 T. Polarization-sensitive photoluminescence measurements on the singlet state of the positively charged trion (X+) in GaAs quantum wells demonstrate a 60% enhancement of the g factor compared to that of the neutral exciton (X-0) in the same sample. This leads to a situation in very high fields where the Zeeman splitting of X+ is sufficiently large to determine whether a state is bound or not, and so calls for a reexamination of what is meant by the binding energy of few particle systems.