Set

A set is a well-defined collection of distinct objects, considered as an object in its own right. The concept of a set is fundamental to mathematics and is used in most branches, including algebra, geometry, and calculus. In set theory, which is a branch of mathematical logic, sets are the primary objects under study. The Hebrew translation for "set" in this context is קבוצה (k'vutza). In other languages, "set" is translated as ensemble in French, conjunto in Spanish, Menge in German, and 集合 (shūgō) in Japanese. Sets can be finite or infinite, and they can contain any kind of objects, including numbers, letters, or even other sets. The objects in a set are called elements or members. A set is said to contain its elements, and an element is said to belong to a set. The relationship of an object being an element of a set is denoted by the symbol "∈". For example, if A is a set containing the elements 1, 2, and 3, then we can write 1 ∈ A, 2 ∈ A, and 3 ∈ A. Sets can be described in two main ways: by listing their elements (roster method) or by describing a property that all elements share (set-builder notation).