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
Equivalences and Partitions, Axiomatic Set Theory 2 2
Defining equivalences and partitions of sets, and proving some theorems about their relations to each other. My Twitter: https://twitter.com/KristapsBalodi3 Equivalence Relations:(0:00) Partitions:(9:22) Connecting Equivalence and Partitions:(14:09) Representatives:(27:04)
From playlist Axiomatic Set Theory
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
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
Orders and Ordered Sets | Axiomatic Set Theory, Section 2.3
We discuss order relations on sets, and isomorphisms of ordered sets. My Twitter: https://twitter.com/KristapsBalodi3
From playlist Axiomatic Set Theory
Set Theory (Part 5): Functions and the Axiom of Choice
Please feel free to leave comments/questions on the video and practice problems below! In this video, I introduce functions as a special sort of relation, go over some function-related terminology, and also prove two theorems involving left- and right-inverses, with the latter theorem nic
From playlist Set Theory by Mathoma
What's so wrong with the Axiom of Choice ?
One of the Zermelo- Fraenkel axioms, called axiom of choice, is remarkably controversial. It links to linear algebra and several paradoxes- find out what is so strange about it ! (00:22) - Math objects as sets (00:54) - What axioms we use ? (01:30) - Understanding axiom of choice (03:2
From playlist Something you did not know...
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
Ex 2: Set Problem Solving - Find the Number of Element in the Union of Two Sets Using a Formula
This example explains how to find the number of elements in the union of two sets using the formula for the cardinality of the union of two sets. Site: http://mathispower4u.com
From playlist Sets
Orders on Sets: Part 1 - Partial Orders
This was recorded as supplemental material for Math 115AH at UCLA in the spring quarter of 2020. In this video, I discuss the concept and definition of a partial order.
From playlist Orders on Sets
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
Set Theory - The first few axioms: Oxford Mathematics 3rd Year Student Lecture
This is the third of four lectures from Robin Knight's 3rd Year Set Theory course. Robin writes: "Infinity baffled mathematicians, and everyone else, for thousands of years. But around 1870, Georg Cantor worked out how to study infinity in a way that made sense, and created set theory. Mo
From playlist Oxford Mathematics Student Lectures - Set Theory
The Simplest Math No One Can Agree on- A Paradox of Choice
To build our mathematics we need a starting point, rules to dictate what we can do and assumed basic truths to serve as a foundation as we seek understanding of higher level problems. But what happens when we can't agree on what we should start with?
From playlist Summer of Math Exposition Youtube Videos
Automated Theorem Proving and Axiomatic Mathematics
Jonathan Gorard
From playlist Wolfram Technology Conference 2019
SEPARATION BUT MATHEMATICALLY: What Types of Mathematical Topologies are there? | Nathan Dalaklis
The title of this video is a bit convoluted. What do you mean by "Separation but Mathematically"? Well, in this video I'll be giving a (very diluted) answer to the question "What types of mathematical topologies are there?" by introducing the separation axioms in topology. The separation
From playlist The New CHALKboard
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