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.

中文翻译：

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人口增长数学中年龄组的相同性

集合论的外延公理指出，任何具有相同成员的两个类都是相同的。然而，在时间 t 年龄为 i 的人群和在 t + l 时年龄为 i + 1 的人群都包括相同的人，具有不同的人口统计属性，因此看起来是两个不同的类别。可以通过明确区分年龄组和队列来解决这一矛盾。队列是在一个时间间隔内构成的众多个体，并贯穿部分时间连续体。另一方面，年龄组只是一个与经验测量相关的参考术语，如出生率或死亡率。因此，t 时的年龄组 i 和 t + 1 时的年龄组 i + 1 这两个概念是不同的。然而，Leslie 和 Lotka 的标准人口增长模型，不支持在年龄组中进行这种区分。最近提出的另一种模型恰恰暗示了这种区别。