Axiom of power set

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

The perfect number of axioms | Axiomatic Set Theory, Section 1.1

In this video we introduce 6 of the axioms of ZFC set theory. My Twitter: https://twitter.com/KristapsBalodi3 Intro: (0:00) The Axiom of Existence: (2:39) The Axiom of Extensionality: (4:20) The Axiom Schema of Comprehension: (6:15) The Axiom of Pair (12:16) The Axiom of Union (15:15) T

From playlist Axiomatic Set Theory

Bonus Video! | Axiomatic Set Theory, Section 1

Proving that the powerset of X is not a subset of X for any set X. My Twitter: https://twitter.com/KristapsBalodi3

From playlist Axiomatic Set Theory

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

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

Proof: Number of Subsets using Induction | Set Theory

We prove that a set A with n elements has 2^n subsets. Thus, we're also proving that the cardinality of a power set is 2 to the power of the cardinality of the set we're taking the power set of. If |A|=n then |P(A)|=2^n. We prove this using mathematical induction. Give it a try yourself -

From playlist Set Theory

Zermelo Fraenkel Powerset

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

Operations on Sets | Axiomatic Set Theory, Section 1.2

We define some basic operations on sets using the axioms of ZFC. My Twitter: https://twitter.com/KristapsBalodi3 Intersection:(0:00) Ordered Tuples/Products:(4:45)

From playlist Axiomatic Set Theory

Determine the Power Set of a Set and the Cardinality of a Power Set

This video explains how to determine a power set of a given set and how to determine the cardinality of a power set.

From playlist Sets (Discrete Math)

Set Theory (Part 2): ZFC Axioms

Please feel free to leave comments/questions on the video and practice problems below! In this video, I introduce some common axioms in set theory using the Zermelo-Fraenkel w/ choice (ZFC) system. Five out of nine ZFC axioms are covered and the remaining four will be introduced in their

From playlist Set Theory by Mathoma

Zermelo Fraenkel Choice

This is part of a series of lectures on the Zermelo-Fraenkel axioms for set theory. We dicuss the axiom of chice, and sketch why it is independent of the other axioms of set theory. For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj52EKVgPi-p50f

From playlist Zermelo Fraenkel axioms

Zermelo Fraenkel Introduction

This lecture is part of an online course on the Zermelo Fraenkel axioms of set theory. This lecture gives an overview of the axioms, describes the von Neumann hierarchy, and sketches several approaches to interpreting the axioms (Platonism, von Neumann hierarchy, multiverse, formalism, pra

From playlist Zermelo Fraenkel axioms

Cantor’s Continuum Hypothesis Set Theory - W. H. Woodin - 2/23/2019

From playlist Linde Hall Inaugural Math Symposium - 2019

The Axiom of Choice and Sets | #some2

The axiom of choice is a powerful tool and underlies a lot of mathematics. But what is this tool? How can we use it? And what do we need to do to get there? Find out more in this video by Proffesional Math LLC! Made for SoME2. More info at https://youtu.be/hZuYICAEN9Y #some2

From playlist Summer of Math Exposition 2 videos

Zermelo Fraenkel Pairing and union

This is part of a series of lectures on the Zermelo-Fraenkel axioms for set theory. We discuss the axioms of pairing and union, the two easiest axioms of ZFC, and consider whether they are really needed. For the other lectures in the course see https://www.youtube.com/playlist?list=PL

From playlist Zermelo Fraenkel axioms

Set Theory 1.1 : Axioms of Set Theory

In this video, I introduce the axioms of set theory and Russel's Paradox. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : http://docdro.id/5ITQHUW

From playlist Set Theory

Relations and Functions | Axiomatic Set Theory, Section 2.1

In this video we define and prove a few basic theorems about relations and functions. My Twitter: https://twitter.com/KristapsBalodi3 Intro:(0:00) Ordered Pairs:(1:43) IMAGE-in that!:(3:33) Composition: (7:57) Functions:(11:05) Special thanks to Alex Stephens

From playlist Axiomatic Set Theory

Axioms of Constructive Set Theory Explained

In this video we're going to discuss the various axiom schemes of constructive set theories and how they relate to type theory. I cover BCST, ECST, IKP, KPI, KP, CST, CZF, IZF, Mac Lane, Z and variants equi-consistent to ETCS from category theory, and then of course ZF and ZFC. The text I

From playlist Logic