Foundations of applied mathematics I

This paper aims to study the foundations of applied mathematics, using a formalized base theory for applied mathematics: ZFCA(sigma) (Zermelo-Fraenkel set theory (with Choice) with atoms, where the subscript used refers to a signature specific to the application. Examples are given, illustrating the following five features of applied mathematics: comprehension principles, application conditionals, representation hypotheses, transfer principles and abstract equivalents.