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
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 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
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
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
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
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 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
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
Foundations S2 - Seminar 8 - Light discussion of soundness, completeness, first vs second order
A seminar series on the foundations of mathematics, by Will Troiani and Billy Snikkers. In this seminar Billy leads a discussion of soundness, completeness and first vs second-order logic, as a recap of some of what has been discussed over the past few months in the seminar. The webpage f
From playlist Foundations seminar
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 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
How ISPs Violate the Laws of Mathematics
Get a free trial of Audible at https://audible.com/minutephysics or by texting 'minutephysics' to 500500 Support MinutePhysics on Patreon! http://www.patreon.com/minutephysics Link to Patreon Supporters: http://www.minutephysics.com/supporters/ MinutePhysics is on twitter - @minutephysic
From playlist MinutePhysics
Anthony Bordg - How to Do Maths Without Dependent Types
What can be done when formalising mathematics without dependent types? I will give you new insights into this question by exploring the capability and possible limitations of the Isabelle/HOL proof assistant. I will explain what we learnt formalising Grothendieck's schemes using only Isabe
From playlist Workshop Schlumberger 2022 : types dépendants et formalisation des mathématiques
Topology Without Tears - Video 2c - Infinite Set Theory
This is the final part, part (c), of Video 2 in a series of videos supplementing the online book "Topology Without Tears" which is available at no cost at www.topologywithouttears.net
From playlist Topology Without Tears
Regularity and non-standard models of arithmetic #PaCE1
Follow-up video: https://youtu.be/7HKnOOvssvs Discussed text, including all links: https://gist.github.com/Nikolaj-K/101c2712dc832dec4991bf568869abc8 Curt's call: https://youtu.be/V93GQaDtv8w Timestamps: 00:00:00 Introduction 00:02:55 Wittgenstein and predicates (optional) 00:11:12 Skolems
From playlist Logic