Zermelo Fraenkel Extensionality
This is part of a series of lectures on the Zermelo-Fraenkel axioms for set theory. In this lecture we discuss the axiom of extensionality, which says that two sets are equal if they have the same elements. For the other lectures in the course see https://www.youtube.com/playlist?list
From playlist Zermelo Fraenkel axioms
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
Axiomatics and the least upper bound property (I) | Real numbers and limits Math Foundations 120
The role of axiomatics in mathematics is a highly contentious one. Originally the term always referred to Euclid, and his use of the term to mean `a self-evident truth that requires no proof '. However in modern times the meaning of the term has shifted dramatically, to the idea that an Ax
From playlist Math Foundations
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 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
FIT2.3.3. Algebraic Extensions
Field Theory: We define an algebraic extension of a field F and show that successive algebraic extensions are also algebraic. This gives a useful criterion for checking algberaic elements. We finish with algebraic closures.
From playlist Abstract Algebra
Algebraic and Transcendental Elements; Finite Extensions - Field Theory - Lecture 01
In this video we introduce the notion of algebraic and transcendental. We then introduce a notion of "finite extension" which will help us prove every element in an extension is algebraic. See @MatthewSalomone's Abstract Algebra 2 videos. They complement this presentation with better exa
From playlist Field Theory
Live CEOing Ep 410: Language Design in Wolfram Language [Combinators]
In this episode of Live CEOing, Stephen Wolfram reviews the design of some upcoming functionality for the Wolfram Language. If you'd like to contribute to the discussion in future episodes, you can participate through this YouTube channel or through the official Twitch channel of Stephen W
From playlist Behind the Scenes in Real-Life Software Design
1.11.11 Set Theory Axioms: Video [Optional]
MIT 6.042J Mathematics for Computer Science, Spring 2015 View the complete course: http://ocw.mit.edu/6-042JS15 Instructor: Albert R. Meyer License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 6.042J Mathematics for Computer Science, Spring 2015
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
Martin Hötzel Escardó: Constructive Mathematics in Univalent Type Theory (Lecture I)
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions
From playlist HIM Lectures: Trimester Program "Types, Sets and Constructions"
Furio Honsell - Tribute to Ennio De Giorgi - 20 September 2016
Honsell, Furio "Implementing Cantor’s paradise in constructive type theory"
From playlist A Mathematical Tribute to Ennio De Giorgi
Axiom of Choice and Regularity each imply LEM
I recommend you go through all parts, but thee AC-LEM proof starts at 55:30. If you skip stuff, still watch the section at 8:22, because I talk in terms of those semantics later. The Regularity-LEM proof at 1:50:55 requires definitions from the earlier AC-LEM proof. Timestamps: 0:00 Intro
From playlist Summer of Math Exposition 2 videos
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
Toward a Computational Interpretation of Univalence - Daniel Licata
Daniel Licata Carnegie Mellon University; Member, School of Mathematics October 18, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
Introduction to Infinite Limits in Calculus 1
Introduction to Infinite Limits in Calculus 1
From playlist Calculus 1 Exam 1 Playlist
Wolfram Physics Project: Axiomatization of the Computational Universe Tuesday, Feb. 16, 2021
This is a Wolfram Physics Project working session about the axiomatization of the Computational Universe. Begins at 1:36 Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this project by visiting our website: http://wolfr.am/physics Check out the announceme
From playlist Wolfram Physics Project Livestream Archive