ABSTRACT
Exchange operations construct the conservation of the invariance of a set through successive intensional and extensional transformations. Negation operations also construct invariance, through inversion or reciprocity, i.e., by generating the fundamental structure of reversibility. Division is the inverse operation of multiplication: it entails partitioning one set into a number of equal subsets. Exchange operations establish the quantitative invariance of a set under transformations affecting its constituent elements. They are therefore an essential component of the number concept. More specifically, exchange operations construct equivalence between two consecutive sets where one element has been varied and the other(s) have been kept constant. Negation is the fundamental operation that constructs identity and it does so by reversing the effects of transformation, and thus allowing the reconstruction of the departing state. The corollary of the developmental pattern might be the quantitatively more extensive excercise of first-order operation seen at least in cebus at the most advanced age.
