Verifiable proof that there is no universal collection
In this video I step through the full formal metamath intuitionistic proof that there is not a collection that contains all collection, in the classical framework cooked up after Zermelo, and assuming just the Bounded Restricted Separation Axiom Schema. Essentially, we derive that for all
From playlist Logic
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
SEPARATION BUT MATHEMATICALLY: What Types of Mathematical Topologies are there? | Nathan Dalaklis
The title of this video is a bit convoluted. What do you mean by "Separation but Mathematically"? Well, in this video I'll be giving a (very diluted) answer to the question "What types of mathematical topologies are there?" by introducing the separation axioms in topology. The separation
From playlist The New CHALKboard
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
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
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 (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
You should know what Impredicativity is.
In this video I discuss the concept of predicativity, impredicativity and vicious circles. The text for the video is found in https://gist.github.com/Nikolaj-K/aae1f4bd582e60e6b7e5b5431fee054c
From playlist Logic
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
Live CEOing Ep 401: Language Design in Wolfram Language [AxiomaticTheory, Echo, FoldWhile, & More]
In this episode of Live CEOing, Stephen Wolfram reviews the design of 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 Wolfra
From playlist Behind the Scenes in Real-Life Software Design
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
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
Axiom of Regularity (Foundation) vs. Induction
Previous video on regularity: https://youtu.be/AqjctCRGxhw Errata: In 56:27 I say Regularity, but I meant to say Replacement. Text and links: https://gist.github.com/Nikolaj-K/bc9f67d685bcc7d1300372cfabceed9b
From playlist Logic
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
Preimage of Composition of Functions Set Theory Proof
Preimage of Composition of Functions Set Theory Proof If you enjoyed this video please consider liking, sharing, and subscribing. You can also help support my channel by becoming a member https://www.youtube.com/channel/UCr7lmzIk63PZnBw3bezl-Mg/join Thank you:)
From playlist Functions, Sets, and Relations
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
Introduction to Predicate Logic
This video introduces predicate logic. mathispower4u.com
From playlist Symbolic Logic and Proofs (Discrete Math)
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