We work in the Alternative Set Theory axiomatics and study relationship between the limits of sequences with a respect to two unequal cuts of the class of natural numbers. A limit taken by a smaller cut we call deficient. Some results obtained below on such a limits allow us to get necessary and sufficient condition for the closure of the family of all measurable classes with a respect to the arbitrary unions.

Key words: cut, measurable class, sequence limit, parafundamentality.