Q has a primitive concept of quasi-cardinal, governed by eight additional axioms, intuitively standing for the quantity of objects in a collection. The quasi-cardinal of a quasi-set is not defined in the usual sense (by means of ordinals) because the m -atoms are assumed (absolutely) indistinguishable. Furthermore, it is possible to define a translation from the language of ZFU into the language of Q in such a way so that there is a 'copy' of ZFU in Q . In this copy, all the usual mathematical concepts can be defined, and the 'sets' (in reality, the ' Q -sets') turn out to be those q-sets whose transitive closure contains no m-atoms.