Sets are the basic objects of mathematics. More precisely every mathematical statement can be written only in terms of sets and symbolic logic. But we have a problem. If sets are the fundaments of mathematics, what are the objects of which sets are made? They are sets as well! As an example, consider the set N of natural numbers. Clearly 2 is an element of N, but can we see 2 as a set? Can we give a meaning to the expression 2∩3 ? The Zermelo-Fraenkel axioms allow us to present every mathematical object as a set and they provide a consistent theory for sets and ultimately for mathematics as a whole. In this second seminar, we present the last four Zermelo-Fraenkel axioms. In particular, we will prove that the universe is not a set and we will define the set of natural numbers.

Mathematics Undergraduate Seminar Series presents: “Introduction to Zermelo-Fraenkel Axioms (Part 2)”

Wednesday, Jan. 28 | 3-3:50 p.m. | Bridges 268

By Damiano Fulghesu, MSUM