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The concept of individuality in quantum mechanics shows radicaldifferences from the concept of individuality in classicalphysics, as E. Schrödinger pointed out in the early steps ofthe theory. Regarding this fact, some authors suggested thatquantum mechanics does not possess its own language, andtherefore, quantum indistinguishability is not incorporated in thetheory from the beginning. Nevertheless, it is possible torepresent the idea of quantum indistinguishability with a firstorder language using quasiset theory (Q). In this work, we showthat Q cannot capture one of the most important features ofquantum non individuality, which is the fact that there arequantum systems for which particle number is not well defined. Anaxiomatic variant of Q, in which quasicardinal is not aprimitive concept (for a kind of quasisets called finitequasisets), is also given. This result encourages the searching oftheories in which the quasicardinal, being a secondary concept,stands undefined for some quasisets, besides showing explicitlythat in a set theory about collections of truly indistinguishableentities, the quasicardinal needs not necessarily be a primitiveconcept.