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
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
The Big (mathematical) Bang | Axiomatic Set Theory, Section 0
The introductory video for a course on the axiomatic theory of ZFC set theory. My Twitter: https://twitter.com/KristapsBalodi3 Intro: (0:00) Russel's Paradox: (2:13)
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
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
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
Set Theory (Part 16): Correspondence Between Number Systems
Please feel free to leave comments/questions on the video and practice problems below! In this video, we will connect the number systems together through isomorphic embedding functions, so that operations are preserved across number systems. I will also argue that, in the strict sense, th
From playlist Set Theory by Mathoma
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 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
Live CEOing Ep 28: Proofs in the Wolfram Language
Watch Stephen Wolfram and teams of developers in a live, working, language design meeting. This episode is about Proofs in the Wolfram Language.
From playlist Behind the Scenes in Real-Life Software Design
Live CEOing Ep 374: Language Design in Wolfram Language [AxiomaticTheory]
In this episode of Live CEOing, Stephen Wolfram discusses upcoming improvements of AxiomaticTheory 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
From playlist Behind the Scenes in Real-Life Software Design
Live CEOing Ep 178: Language Design in Wolfram Language
Watch Stephen Wolfram and teams of developers in a live, working, language design meeting. This episode is about Language Design in the Wolfram Language.
From playlist Behind the Scenes in Real-Life Software Design
Automated Theorem Proving and Axiomatic Mathematics
Jonathan Gorard
From playlist Wolfram Technology Conference 2019
Barber & Russell Paradoxes (History of Undecidability Part 2) - Computerphile
$20 off your 1st purchase at www.LittleBits.com use the code “COMPUTERPHILE” The Barber Paradox: Professor Brailsford continues the history of undecidability. History of Undecidability Part1: http://youtu.be/nsZsd5qtbo4 Turing & The Halting Problem: http://youtu.be/macM_MtS_w4 http://
From playlist The History of Undecidability
Wolfram Physics Project: a Conversation on Current Work (Jan. 26, 2021)
This is a Wolfram Physics Project conversation on our continuing efforts to make progress on the fundamental theory of physics. Begins at 3:00 Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this project by visiting our website: http://wolfr.am/physics Ch
From playlist Wolfram Physics Project Livestream Archive
Live CEOing Ep 112: Language Design in Wolfram Language
Watch Stephen Wolfram and teams of developers in a live, working, language design meeting. This episode is about Language Design in the Wolfram Language.
From playlist Behind the Scenes in Real-Life Software Design
Live CEOing Ep 380: FindGeometricProof Design Review for Wolfram Language
In this episode of Live CEOing, Stephen Wolfram reviews the design of FindGeometricProof 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 Wolfram he
From playlist Behind the Scenes in Real-Life Software Design
Jean-Yves Girard: Deux ou trois choses que je sais d’elle : la logique
HYBRID EVENT Recorded during the meeting Linear Logic Winter School" the January 28, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual
From playlist Logic and Foundations
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...