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
Introduction to sets || Set theory Overview - Part 2
A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other #sets. The #set with no element is the empty
From playlist 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
Set Theory (Part 3): Ordered Pairs and Cartesian Products
Please feel free to leave comments/questions on the video and practice problems below! In this video, I cover the Kuratowski definition of ordered pairs in terms of sets. This will allow us to speak of relations and functions in terms of sets as the basic mathematical objects and will ser
From playlist Set Theory by Mathoma
Introduction to sets || Set theory Overview - Part 1
A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other #sets. The #set with no element is the empty
From playlist Set Theory
Set Theory (Part 4): Relations
Please feel free to leave comments/questions on the video and practice problems below! In this video, the notion of relation is discussed, using the interpretation of a Cartesian product as forming a grid between sets and a relation as any subset of points on this grid. This will be an im
From playlist Set Theory by Mathoma
Towards elementary infinity-toposes - Michael Shulman
Vladimir Voevodsky Memorial Conference Topic: Towards elementary infinity-toposes Speaker: Michael Shulman Affiliation: University of San Diego Date: September 13, 2018 For more video please visit http://video.ias.edu
From playlist Mathematics
Tom Leinster : The categorical origins of entropy
Recording during the thematic meeting : "Geometrical and Topological Structures of Information" the August 29, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent
From playlist Geometry
On finite dimensional omega-categorical structures (...) - P. Simon - Workshop 1 - CEB T1 2018
Pierre Simon (Berkeley) / 31.01.2018 On finite dimensional omega-categorical structures and NIP theories The study of omega-categorical structures lies at the intersection of model theory, combinatorics and group theory. Some classes of omega-categorical structures have been classified,
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields
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
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
Galois theory: Transcendental extensions
This lecture is part of an online graduate course on Galois theory. We describe transcendental extension of fields and transcendence bases. As applications we classify algebraically closed fields and show hw to define the dimension of an algebraic variety.
From playlist Galois theory
How to diagonalize a functor - Benjamin Elias
Members' Seminar Topic: How to diagonalize a functor Speaker: Benjamin Elias Affiliation: University of Oregon; von Neumann Fellow, School of Mathematics Date: October 5, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
R & Python - Conditional Inference Trees
Lecturer: Dr. Erin M. Buchanan Summer 2020 https://www.patreon.com/statisticsofdoom This video is part of my human language modeling class - this video set covers the updated version with both R and Python. This video explores the use of conditional inference trees and random forests to
From playlist Human Language (ANLY 540)
Set Theory Proof: A subset of B and C subset of D then A x C is a subset of B x D
Set Theory Proof: A subset of B and C subset of D then A x C is a subset of B x D This is an example of a rigorous set theory proof with all steps shown.
From playlist Set Theory
What is a Group Action? : A Group as a Category and The Skeleton Operation ☠
This week I try to take a more Categorical approach to answering and expanding upon the question of "what is a group action". Along the way I'll go over thinking about a group as a category and eventually hit on the skeleton operation on a category and use it to present an example of the c
From playlist The New CHALKboard
LambdaConf 2015 - Type Theory and its Meaning Explanations Jon Sterling
At the heart of intuitionistic type theory lies an intuitive semantics called the “meaning explanations." Crucially, when meaning explanations are taken as definitive for type theory, the core notion is no longer “proof” but “verification”. We’ll explore how type theories of this sort aris
From playlist LambdaConf 2015
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
Automorphism groups and Ramsey properties of sparse graphs - D. Evans - Workshop 1 - CEB T1 2018
David Evans (Imperial) / 30.01.2018 An infinite graph is sparse if there is a positive integer k such that for every finite subgraph, the number of edges is bounded above by k times the number of vertices. Such graphs arise in model theory via Hrushovskis predimension constructions. In jo
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields