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
Introduction to sets || Set theory Overview - Part 2
A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other #sets. The #set with no element is the empty
From playlist 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
Introduction to sets || Set theory Overview - Part 1
A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other #sets. The #set with no element is the empty
From playlist Set Theory
Introduction to Set Theory (Discrete Mathematics)
Introduction to Set Theory (Discrete Mathematics) This is a basic introduction to set theory starting from the very beginning. This is typically found near the beginning of a discrete mathematics course in college or at the beginning of other advanced mathematics courses. ***************
From playlist 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
How to Identify the Elements of a Set | Set Theory
Sets contain elements, and sometimes those elements are sets, intervals, ordered pairs or sequences, or a slew of other objects! When a set is written in roster form, its elements are separated by commas, but some elements may have commas of their own, making it a little difficult at times
From playlist Set Theory
Set Theory (Part 2b): The Bogus Universal Set
Please feel free to leave comments/questions on the video below! In this video, I argue against the existence of the set of all sets and show that this claim is provable in ZFC. This theorem is very much tied to the Russell Paradox, besides being one of the problematic ideas in mathematic
From playlist Set Theory by Mathoma
Inernal Languages for Higher Toposes - Michael Shulman
Michael Shulman University of California, San Diego; Member, School of Mathematics October 3, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
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
A topos-theoretic view of difference algebra
From playlist Workshop on Model Theory, Differential/Difference Algebra, and Applications
David Michael ROBERTS - Class forcing and topos theory
It is well-known that forcing over a model of material set theory co rresponds to taking sheaves over a small site (a poset, a complete Boolean algebra, and so on). One phenomenon that occurs is that given a small site, all new subsets created are smaller than a fixed bound depending on th
From playlist Topos à l'IHES
Rahim Moosa: Nonstandard compact complex manifolds with a generic auto-morphism
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Logic and Foundations
Joshua Wrigley - The Logic and Geometry of Localic Morphisms
Talk at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Slides: https://aroundtoposes.com/wp-content/uploads/2021/07/WrigleySlidesToposesOnline.pdf In this presentation, a substitutive syntactic site for the classifying topos of a ge
From playlist Toposes online
Simplicial Types - Peter Lumsdaine
Peter Lumsdaine Dalhousie University; Member, School of Mathematics January 16, 2013 For more videos, visit http://video.ias.edu
From playlist Mathematics
Cohomology in difference algebra and geometry We view difference algebra as the study of algebraic objects in the topos of difference sets, i.e., as `ordinary algebra’ in a new universe. The methods of topos theory and categorical logic enable us to develop difference homological algebra,
From playlist DART X
Ingo BLECHSCHMIDT - Using the internal language of toposes in algebraic geometry
We describe how the internal language of certain toposes, the associated petit and gros Zariski toposes of a scheme, can be used to give simpler denitions and more conceptual proofs of the basic notions and observations in algebraic geometry. The starting point is that, from the internal p
From playlist Topos à l'IHES
What is the complement of a set? Sets in mathematics are very cool, and one of my favorite thins in set theory is the complement and the universal set. In this video we will define complement in set theory, and in order to do so you will also need to know the meaning of universal set. I go
From playlist Set Theory
Ximena Fernández 7/20/22: Morse theory for group presentations and the persistent fundamental group
Discrete Morse theory is a combinatorial tool to simplify the structure of a given (regular) CW-complex up to homotopy equivalence, in terms of the critical cells of discrete Morse functions. In this talk, I will present a refinement of this theory that guarantees not only a homotopy equiv
From playlist AATRN 2022