Axiomatic set theory

Axiomatic set theory is a form of mathematics that tries to explain how sets, or groups of objects, work. It is based on certain assumptions, known as axioms, that are accepted without proof. These axioms describe how sets can be combined, how things behave when you add or remove objects to/from sets, and how to tell if two sets have the same number of objects. Axiomatic set theory is used by mathematicians to help answer many types of questions, such as how to prove that two things are equal, or how to determine if two sets of objects can be combined together. By understanding the axioms, mathematicians can make logical deductions and solve mathematical problems.