Starred sections below are op-tional. They discuss interesting mathematics connected to concepts covered in the course. Thanks to Cecelia Higgins, Jacob Manaker, Forte Shinko, Marlon Trifunovic, …

Jul 23, 2025 · This section introduces the basics of Set Theory, helping you understand key concepts like types of sets, set operations, and important formulas through clear examples and symbols.

Although set theory can be considered within a single first-order language, with only non- logical constant ∈, it is convenient to have more complicated languages, corresponding to the many …

These notes for a graduate course in set theory are on their way to be-coming a book. They originated as handwritten notes in a course at the University of Toronto given by Prof. William Weiss.

This chapter introduces set theory, mathematical in-duction, and formalizes the notion of mathematical functions. The material is mostly elementary. For those of you new to abstract mathematics …

There is no repetition in a set, meaning each element must be unique. You could, for example, have variations on an element, such as a regular number 4 and a boldface number 4. There is no order in …

subset of any set. In particular, this means that the power set of any set is itself never empty since it at least con ains the empty set. In the example above, A had three elements and P(A)