From naive infinitesimal analysis to the axiomatic formulation of non-standard analysis

It is planned to discuss the process of the evolution of the principle of exhaustion through the concept of an infinitesimal value to non-standard analysis by Robinson and his modern upgrades. Will focus on the development of the concepts of a real number, modeling the properties of real numbers in the theory of hyper-rational numbers, the connection with the concept of constructive real number and computations.