Set Theory and Foundations of Mathematics

Set theory is a branch of mathematics that studies collections of objects called sets, which can contain anything—numbers, points, or even other sets. It provides a fundamental framework for understanding and building all mathematical concepts. Foundations of mathematics involve establishing the basic principles and logical rules—like how sets relate and how numbers are defined—that ensure mathematics is consistent and rigorous. Together, they underpin the entire structure of modern mathematics, enabling precise reasoning and formal proofs across various mathematical disciplines.