What do you mean by set theory?
Set theory is the mathematical theory of well-determined collections, called sets, of objects that are called members, or elements, of the set. So, the essence of set theory is the study of infinite sets, and therefore it can be defined as the mathematical theory of the actual—as opposed to potential—infinite.
Who is father of set theory?
Georg Ferdinand Ludwig Philipp Cantor
Georg Cantor, in full Georg Ferdinand Ludwig Philipp Cantor, (born March 3, 1845, St. Petersburg, Russia—died January 6, 1918, Halle, Germany), German mathematician who founded set theory and introduced the mathematically meaningful concept of transfinite numbers, indefinitely large but distinct from one another.
What is sets and examples?
What is set? A set is a collection of elements or numbers or objects, represented within the curly brackets { }. For example: {1,2,3,4} is a set of numbers.
What are basic concepts of set theory?
Basic Concepts of Set Theory Union of Sets: Union of two or more sets is the set of all elements that belong to any of these sets. Intersection of Sets: It is the set of all the elements, which are common to all the sets. Difference of two sets: A – B = {x: x ∈ A and x ∉ B}.
What are some examples of set theory?
Quoting Set theory: Many mathematical concepts can be defined precisely using only set theoretic concepts. For example, mathematical structures as diverse as graphs, manifolds, rings, and vector spaces can all be defined as sets satisfying various (axiomatic) properties.
What are axioms of set theory?
In axiomatic set theory, the axioms themselves are the definition of the notion of a set: A set is whatever behaves like the axioms say sets behave. This assertion clashes with my (admittedly limited) understanding of how first-order logic, model theory, and axiomatic set theories work.
What are some real-life applications of set theory?
In Kitchen. Kitchen is the most relevant example of sets.