What is a Power Set? | Set Theory, Subsets, Cardinality
What is a power set? A power set of any set A is the set containing all subsets of the given set A. For example, if we have the set A = {1, 2, 3}. Then the power set of A, denoted P(A), is {{ }, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}} where { } is the empty set. We also know that
From playlist Set Theory
Power Set of the Power Set of the Power Set of the Empty Set | Set Theory
The power set of the power set of the power set of the empty set, we'll go over how to find just that in today's set theory video lesson! We'll also go over the power set of the empty set, the power set of the power set of the empty set, and we'll se the power set of the power set of the p
From playlist Set Theory
Every Set is an Element of its Power Set | Set Theory
Every set is an element of its own power set. This is because the power set of a set S, P(S), contains all subsets of S. By definition, every set is a subset of itself, and thus by definition of the power set of S, it must contain S. This is even true for the always-fun empty set! We discu
From playlist Set Theory
Finding Power Set Examples | Set Theory, Subsets and Power Sets
How do we find the power set of a set? That's what we'll go over in today's set theory video lesson with 4 examples! Remember the power set of a set S is the set P(S) consisting of all subsets of S. Don't forget to include the empty set and the set S itself! Also recall that the cardinali
From playlist Set Theory
How to Find a Minimal Generating Set
How to Find a Minimal Generating Set
From playlist Linear Algebra
Power Set of the Math Set {m, a, t, h} | Set Theory
We find the power set of the set {m, a, t, h}, going over strategies and the general method to use for finding power sets. #SetTheory Recall the power set of a set S, P(S), is the set of all subsets of S. Thus, the cardinality of the power set of S is the number of subsets of S, which is
From playlist Set Theory
Listing Subsets Using Tree Diagrams | Set Theory, Subsets, Power Sets
Here is a method for completely listing the subsets of a given set using tree diagrams. It's a handy way to make sure you don't miss any subsets when trying to find them. It's not super efficient, but it is reliable! The process is pretty simple, we begin with the empty set, and then branc
From playlist Set Theory
This is part of a series of lectures on the Zermelo-Fraenkel axioms for set theory. We discuss the powerset axiom, the strongest of the ZF axioms, and explain why the notion of a powerset is so hard to pin down precisely. For the other lectures in the course see https://www.youtube.com
From playlist Zermelo Fraenkel axioms
Listing elements from a set (2)
Powered by https://www.numerise.com/ Listing elements from a set (2)
From playlist Set theory
Luca Motto Ros: Towards the « right » generalization of descriptive set theory to...
Recording during the meeting "15th International Luminy Workshop in Set Theory" the September 26, 2019 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's A
From playlist Logic and Foundations
Christian Gaetz: "Antichains and intervals in the weak order"
Asymptotic Algebraic Combinatorics 2020 "Antichains and intervals in the weak order" Christian Gaetz - Massachusetts Institute of Technology Abstract: The weak order is the partial order on the symmetric group S_n (or other Coxeter group) whose cover relations correspond to simple transp
From playlist Asymptotic Algebraic Combinatorics 2020
The Generalized Ramanujan Conjectures and Applications (Lecture 2) by Peter Sarnak
Lecture 2: Thin Groups and Expansion Abstract: Infinite index subgroups of matrix groups like SL(n,Z) which are Zariski dense in SL(n), arise in many geometric and diophantine problems (eg as reflection groups,groups connected with elementary geometry such as integral apollonian packings,
From playlist Generalized Ramanujan Conjectures Applications by Peter Sarnak
Thin Matrix Groups - a brief survey of some aspects - Peter Sarnak
Speaker: Peter Sarnak (Princeton/IAS) Title: Thin Matrix Groups - a brief survey of some aspects More videos on http://video.ias.edu
From playlist Mathematics
Sergey Melikhov, Steklov Math Institute (Moscow) Title: Fine Shape Abstract: A shape theory is something which is supposed to agree with homotopy theory on polyhedra and to treat more general spaces by looking at their polyhedral approximations. Or if you prefer, it is something which is s
From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022
Strong minimality for Painleve equations and Fuchsian equations Strong minimality is a central notion in model theory which has an interpretation in differential algebra as a functional transcendence statement. We will talk about some new proofs of strong minimality for differential equat
From playlist DART X
Diophantine Analysis of affine cubic Markoff type Surfaces - Peter Sarnak
Speaker: Peter Sarnak (Princeton/IAS) Title: Diophantine Analysis of affine cubic Markoff type Surfaces More videos on http://video.ias.edu
From playlist Mathematics
Title: Differential Fields—A Model Theorist's View May 2016 Kolchin Seminar Workshop
From playlist May 2016 Kolchin Seminar Workshop
Title: Trichotomy Principle for Partial Differential Fields May 2016 Kolchin Seminar Workshop
From playlist May 2016 Kolchin Seminar Workshop
Empty Set vs Set Containing Empty Set | Set Theory
What's the difference between the empty set and the set containing the empty set? We'll look at {} vs {{}} in today's set theory video lesson, discuss their cardinalities, and look at their power sets. As we'll see, the power set of the empty set is our friend { {} }! The river runs peacef
From playlist Set Theory
Commutative algebra 31 (Nullstellensatz)
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We describe the weak and strong Nullstellensatz, and give short proofs of them over the complex numbers using Rabinowitsch's
From playlist Commutative algebra