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Sameness of Age Cohorts in the Mathematics of Population Growth

The axiom of extensionality of set theory states that any two classes that have identical members are identical. Yet the class of persons age i at time t and the class of persons age i + 1 at t + l, both including same persons, possess different demographic attributes, and thus appear to be two different classes. The contradiction could be resolved by making a clear distinction between age groups and cohorts. Cohort is a multitude of individuals, which is constituted within a time interval, and endures throughout part of the time continuum. Age group, on the other hand, is only a reference term to which empirical measurement relates, as in birth or death rates. Accordingly, the two concepts, age group i at t, and age group i + 1 at t + 1, are different. The standard population growth model of Leslie and Lotka, however, does not support such a distinction in age groups. An alternative model, proposed recently, implies precisely such a distinction.