The Elements of Set Theory

Set theory is the mathematical study of collections of objects called sets. Elements are the individual items within these sets. Sets are usually defined by listing their elements or describing a property they share. For example, the set of all natural numbers includes 0, 1, 2, and so on. Operations like union (combining sets), intersection (common elements), and difference (elements in one set but not the other) help analyze relationships between sets. Set theory provides a foundational language for mathematics, allowing precise discussion of collections and their properties, essential for fields ranging from logic to computer science.