**Contents**

- Axioms
- Operations on Sets
- Cartesian Product, Relation and Function
- Infinite Union and Intersection
- Orders
- Induction and Recursion
- Axiom of Choice and Its Equivalents
- Cardinality without Axiom ZF9
- Ordinals and Cardinals with Axiom ZF9
- Natural Infinite Set and Countability Definition
- Axioms of Natural Numbers