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2022-08 NITheCS Mini-School: Amartya Goswami and Zurab Janelidze, Elementary Introduction to Set Theory

2022-08 NITheCS Mini-School

Prof Amartya Goswami and Prof Zurab Janelidze

Elementary Introduction to Set Theory

Abstract: The aim of this mini-school is to give a very basic introduction to set theory, a mathematical "theory of everything". No prior experience in mathematics is required for most of the lectures. Set theory is, on one hand, a theory of infinity, and on the other hand, a uniform intuitive language for describing any scientific phenomenon that can be rigorously formalized. Set theory is based on the idea that any mathematical structure can be decomposed into more basic constituents, called its elements. By studying the organization of elements (and possibly their elements, and their elements, and so on), it becomes possible to understand the essence and function of a given mathematical structure. This point of view may seem opposite to the approach of category theory, which tries to study mathematical structures in terms of their interaction with other structures, rather than by looking at elements within those structures. However, the two theories are in fact intimately related. We will touch on this relationship in the context of the concepts of category theory dealt with in the 2021 NITheCS mini-school "Elementary Introduction to Category Theory".