Elementary Mathematics from an Advanced Standpoint 1

The aim of this course is to provide an introduction to the axiomatic Zermelo-Fraenkel Set Theory. The notions of finite and infinite sets, natural numbers, ordinals and cardinals will be given and studied, together with the related arithmetics. Furthermore, various equivalent forms of The Axiom of Choice will be given, highlighting the importance of such an axiom from both a foundational and a practical point of view.

Acquisition of awareness of the need for a formal, rigorous and axiomatic theory of sets, in contrast to the naive set theory, usually taken as a basis for mathematics. Critical capacity to use axioms and comprehension of the role of paradoxes.