Introduction
Set theory is a branch of mathematics that deals with the properties of well-defined collections of objects, such as numbers or functions. It was created by Georg Cantor in the 19th century and has an axiomatic basis for treating infinite sets as mathematical objects.
Content
Sets and Relations
Sets and Axioms
Construction of Sets
Relations and Functions
Composition Laws
Equinumerous and Countability
Cardinality
Cantor Set
Number Systems
Order Theory
Preorder, Partial Order and Posets
Preorder and Posets
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Acknowledgement
This part is mainly based on the ANU course MATH1005 in 2022 and MATH2320 in 2024.