Besides its foundational role, set theory also provides the framework to develop a mathematical theory of infinity, and has various applications in computer science (such as in the theory of relational …

Set Theory is the true study of infinity. This alone assures the subject of a place prominent in human culture. But even more, Set Theory is the milieu in which mathematics takes place today. As such, it …

Set theory began with Cantor's proof in 1874 that the natural numbers do not have the same cardinality as the real numbers. Cantor's original motivation was to give a new proof of Liouville's theorem that …

Oct 8, 2014 · Set theory is the mathematical theory of well-determined collections, called sets, of objects that are called members, or elements, of the set. Pure set theory deals exclusively with sets, so the …

Oct 30, 2025 · Set theory, branch of mathematics that deals with the properties of well-defined collections of objects such as numbers or functions. The theory is valuable as a basis for precise and …

Jul 23, 2025 · This section introduces the basics of Set Theory, helping you understand key concepts like types of sets, set operations, and important formulas through clear examples and symbols.

At its most basic level, set theory describes the relationship between objects and whether they are elements (or members) of a given set. Sets are also objects, and thus can also be related to each …

Although set theory can be considered within a single first-order language, with only non- logical constant ∈, it is convenient to have more complicated languages, corresponding to the many …

Sets are a useful vocabulary in many areas of mathematics. They provide a language for stating interesting results. For example, in analysis: “a monotone function from ‘ to ‘ is continuous except, at …

Mar 19, 2010 · The concept of a set is one of the most fundamental ideas in mathematics. Essentially, a set is simply a collection of objects. The field of mathematics that studies sets, called set theory, was …