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
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
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
Foundations of Quantum Mechanics: Completeness
Foundations of Quantum Mechanics: Completeness This lecture is a long and complex proof that every finite vector space is complete. The purpose is to demonstrate some of the methods of real and functional analysis as well as to emphasize the significance of a vector space being finite-dim
From playlist Mathematical Foundations of Quantum Mechanics
Topological Spaces: Introduction & Axioms
The first video in a new series on topological spaces and manifolds.
From playlist Topology & Manifolds
Definition of a Topological Space
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definition of a Topological Space
From playlist Topology
This video lists an explains propositional, predicate calculus axioms, as well as a set theoretical statement that goes with it, including ZF and beyond. Where possible, the explanations are kept constructive. You can find the list of axioms in the file discussed in this video here: https:
From playlist Logic
The rising sea: Grothendieck on simplicity and generality - Colin McLarty [2003]
Slides for this talk: https://drive.google.com/file/d/1yDmqhdcKo6-YpDpRdHh2hvuNirZVbcKr/view?usp=sharing Notes for this talk: https://drive.google.com/open?id=1p45B3Hh8WPRhdhQAd0Wq0MvmY0JYSnmc The History of Algebra in the Nineteenth and Twentieth Centuries April 21 - 25, 2003 Colin Mc
From playlist Mathematics
This video is about topological spaces and some of their basic properties.
From playlist Basics: Topology
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
Wolfram Physics Project: Working Session Tuesday, Nov. 2, 2021 [Topos Theory]
This is a Wolfram Physics Project working session about Topos Theory in the Wolfram Model. 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 announcement post: http://wolfr.am/
From playlist Wolfram Physics Project Livestream Archive
Univalent Foundations Seminar - Steve Awodey
Steve Awodey Carnegie Mellon University; Member, School of Mathematics November 19, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
The Most Infamous Topology Book
This is probably the most infamous book on topology. The book is General Topology and it was written by Wolfgang Franz. This is the book on amazon: https://amzn.to/368bAzP Note this is my affiliate link, so please use this is you decide to purchase the book. Apparently it is very inexp
From playlist Cool Math Stuff
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
Wolfram Physics Project: Working Session Tuesday, Nov. 16, 2021 [Metamathematics]
This is a Wolfram Physics Project working session on metamathematics in the Wolfram Model. 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 announcement post: http://wolfr.am/
From playlist Wolfram Physics Project Livestream Archive
Francesco Ciraulo: Notions of Booleanization in pointfree Topology
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: Boolean algebras play a key role in the foundations of classical mathematics. And a similar role is played by Heyting algebras for constructive mathematics. But this is
From playlist Workshop: "Constructive Mathematics"
Cyril Cohen - Hierarchy Builder
Libraries of machine checked code are, nowadays, organized around hierarchies of algebraic structures. Unfortunately the language of Type Theory and the features provided by modern proof assistants make the construction of a hierarchy hard even for expert users. The difficulty begins with
From playlist Workshop Schlumberger 2022 : types dépendants et formalisation des mathématiques
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
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
