Introduction to the Cardinality of Sets and a Countability Proof
Introduction to Cardinality, Finite Sets, Infinite Sets, Countable Sets, and a Countability Proof - Definition of Cardinality. Two sets A, B have the same cardinality if there is a bijection between them. - Definition of finite and infinite sets. - Definition of a cardinal number. - Discu
From playlist Set Theory
Determine the Cardinality of Sets From a List of Set
This video explains how to determine the cardinality of sets given as lists. It includes union, intersection, and complement of sets. http://mathispower4u.com
From playlist Sets
What is the Cardinality of a Set? | Set Theory, Empty Set
What is the cardinality of a set? In this video we go over just that, defining cardinality with examples both easy and hard. To find the cardinality of a set, you need only to count the elements in the set. The cardinality of the empty set is 0, the cardinality of the set A = {0, 1, 2} is
From playlist Set Theory
The Cardinality of the Union of Three Sets
This video provides an explanation of the formula for the cardinality of the union of three sets.
From playlist Counting (Discrete Math)
BM9.1. Cardinality 1: Finite Sets
Basic Methods: We define cardinality as an equivalence relation on sets using one-one correspondences. In this talk, we consider finite sets and counting rules.
From playlist Math Major Basics
BM9.2. Cardinality 2: Infinite Sets
Basic Methods: We continue the study of cardinality with infinite sets. First the class of countably infinite sets is considered, and basic results given. Then we give examples of uncountable sets using Cantor diagonalization arguments.
From playlist Math Major Basics
Finding Cardinalities of Sets | Set Theory
Let's find the cardinality of some simple sets in set builder notation! Recall the cardinality of a set is simply the number of elements it contains. We'll write some sets that have been given in set builder notation and identify their cardinalities. We also briefly discuss the cardinality
From playlist Set Theory
Fundamentals of Mathematics - Lecture 31: The Power Set of the Naturals, Cardinality Continuum
course page: https://www.uvm.edu/~tdupuy/logic/Math52-Fall2017.html videography - Eric Melton (UVM)
From playlist Fundamentals of Mathematics
What is infinity? Can there be different sizes of infinity? Surprisingly, the answer is yes. In fact, there are many different ways to make bigger infinite sets. In this video, a few different sets of infinities will be explored, including their surprising differences and even more surpris
From playlist Summer of Math Exposition 2 videos
Does Infinite Cardinal Arithmetic Resemble Number Theory? - Menachem Kojman
Menachem Kojman Ben-Gurion University of the Negev; Member, School of Mathematics February 28, 2011 I will survey the development of modern infinite cardinal arithmetic, focusing mainly on S. Shelah's algebraic pcf theory, which was developed in the 1990s to provide upper bounds in infinit
From playlist Mathematics
Colloquium MathAlp 2018 - Patrick Dehornoy
La théorie des ensembles cinquante ans après Cohen : On présentera quelques résultats de théorie des ensembles récents, avec un accent sur l'hypothèse du continu et la possibilité de résoudre la question après les résultats négatifs bien connus de Gödel et Cohen, et sur les tables de Lave
From playlist Colloquiums MathAlp
David Michael ROBERTS - Class forcing and topos theory
It is well-known that forcing over a model of material set theory co rresponds to taking sheaves over a small site (a poset, a complete Boolean algebra, and so on). One phenomenon that occurs is that given a small site, all new subsets created are smaller than a fixed bound depending on th
From playlist Topos à l'IHES
A road to the infinities: Some topics in set theory by Sujata Ghosh
PROGRAM : SUMMER SCHOOL FOR WOMEN IN MATHEMATICS AND STATISTICS ORGANIZERS : Siva Athreya and Anita Naolekar DATE : 13 May 2019 to 24 May 2019 VENUE : Ramanujan Lecture Hall, ICTS Bangalore The summer school is intended for women students studying in first year B.A/B.Sc./B.E./B.Tech.
From playlist Summer School for Women in Mathematics and Statistics 2019
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
Real Analysis Ep 6: Countable vs uncountable
Episode 6 of my videos for my undergraduate Real Analysis course at Fairfield University. This is a recording of a live class. This episode is about countable and uncountable sets, Cantor's theorem, and the continuum hypothesis. Class webpage: http://cstaecker.fairfield.edu/~cstaecker/c
From playlist Math 3371 (Real analysis) Fall 2020
Should the power class of any non-empty set even be a set? It's not in constructive Zermelo-Fraenkel, but once you add the Axiom of Choice you end up in ZFC where you have to assign it a cardinal number. But then, well-orderings on something like the reals provably exist that are not descr
From playlist Logic
Gabriel Goldberg: The Jackson analysis and the strongest hypotheses
HYBRID EVENT Recorded during the meeting "XVI International Luminy Workshop in Set Theory" the September 13, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematician
From playlist Logic and Foundations
Cardinality Example with [0,1]
Real Analysis: We show that the sets [0,1], (0,1], and (0,1) have the cardinality by constructing one-one correspondences. Then we expand the method to construct a one-one correspondence between [0,1] and the irrationals in [0,1].
From playlist Real Analysis
Saharon Shelah : Categoricity of atomic classes in small cardinals, in ZFC
CONFERENCE Recording during the thematic meeting : « Discrete mathematics and logic: between mathematics and the computer science » the January 17, 2023 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Jean Petit Find this video and other talks give
From playlist Logic and Foundations