In the mathematical field of set theory, an ideal is a partially ordered collection of sets that are considered to be "small" or "negligible". Every subset of an element of the ideal must also be in the ideal (this codifies the idea that an ideal is a notion of smallness), and the union of any two elements of the ideal must also be in the ideal. More formally, given a set an ideal on is a nonempty subset of the powerset of such that: 1. * 2. * if and then and 3. * if then Some authors add a fourth condition that itself is not in ; ideals with this extra property are called proper ideals. Ideals in the set-theoretic sense are exactly ideals in the order-theoretic sense, where the relevant order is set inclusion. Also, they are exactly ideals in the ring-theoretic sense on the Boolean ring formed by the powerset of the underlying set. The dual notion of an ideal is a filter. (Wikipedia).
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
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
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
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
We give some basic definitions and notions associated with sets. In particular, we describe sets via the "roster method", via a verbal description, and with set-builder notation. We also give an example of proving the equality of two sets. Please Subscribe: https://www.youtube.com/michael
From playlist Proof Writing
This video introduces the basic vocabulary used in set theory. http://mathispower4u.wordpress.com/
From playlist Sets
Basic Methods: We introduce basic notions from naive set theory, including sets, elements, and subsets. We give examples of showing two sets are equal by mutual inclusion. Then we define the power set and note Russell's paradox.
From playlist Math Major Basics
Visual Group Theory, Lecture 7.2: Ideals, quotient rings, and finite fields
Visual Group Theory, Lecture 7.2: Ideals, quotient rings, and finite fields A left (resp., right) ideal of a ring R is a subring that is invariant under left (resp., right) multiplication. Two-sided ideals are those that are both left and right ideals. This is the analogue of normal subgr
From playlist Visual Group Theory
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
Introduction to the category of Adic spaces (Lecture 1) by Utsav Choudhury
PERFECTOID SPACES ORGANIZERS: Debargha Banerjee, Denis Benois, Chitrabhanu Chaudhuri, and Narasimha Kumar Cheraku DATE & TIME: 09 September 2019 to 20 September 2019 VENUE: Madhava Lecture Hall, ICTS, Bangalore Scientific committee: Jacques Tilouine (University of Paris, France) Eknath
From playlist Perfectoid Spaces 2019
Antonino Iannazzo, Queen Mary University of London
March 3, Antonino Iannazzo, Queen Mary University of London Differential Algebraic Geometry
From playlist Spring 2023 Online Kolchin Seminar in Differential Algebra
Representations of Galois algebras – Vyacheslav Futorny – ICM2018
Lie Theory and Generalizations Invited Lecture 7.3 Representations of Galois algebras Vyacheslav Futorny Abstract: Galois algebras allow an effective study of their representations based on the invariant skew group structure. We will survey their theory including recent results on Gelfan
From playlist Lie Theory and Generalizations
An introduction to modified traces, Jonathan Kujawa, Lecture I
Lecture series on modified traces in algebra and topology The trace of a map and the dimension of a representation are fundamental invariants in representation theory. They are useful both for proving results in representation theory and for applications in other areas (e.g., low-dimensio
From playlist Lecture series on modified traces in algebra and topology
Boris Springborn: Discrete Uniformization and Ideal Hyperbolic Polyhedra
CATS 2021 Online Seminar Boris Springborn, Technical University of Berlin Abstract: This talk will be about two seemingly unrelated problems: 00:46:00 A discrete version of the uniformization problem for piecewise flat surfaces, and 00:35:48 Constructing ideal hyperbolic polyhedra with p
From playlist Computational & Algorithmic Topology (CATS 2021)
D-modules in birational geometry – Mihnea Popa – ICM2018
Algebraic and Complex Geometry Invited Lecture 4.10 D-modules in birational geometry Mihnea Popa Abstract: I will give an overview of techniques based on the theory of mixed Hodge modules, which lead to a number of applications of a rather elementary nature in birational and complex geom
From playlist Algebraic & Complex Geometry
Dan-Virgil Voiculescu: Around the Quasicentral Modulus
Talk by Dan-Virgil Voiculescu in Global Noncommutative Geometry Seminar (Americas) https://globalncgseminar.org/talks/tba-9/ on March 26, 2021.
From playlist Global Noncommutative Geometry Seminar (Americas)
Kevin Buzzard (lecture 10/20) Automorphic Forms And The Langlands Program [2017]
Full course playlist: https://www.youtube.com/playlist?list=PLhsb6tmzSpiysoRR0bZozub-MM0k3mdFR http://wwwf.imperial.ac.uk/~buzzard/MSRI/ Summer Graduate School Automorphic Forms and the Langlands Program July 24, 2017 - August 04, 2017 Kevin Buzzard (Imperial College, London) https://w
From playlist MSRI Summer School: Automorphic Forms And The Langlands Program, by Kevin Buzzard [2017]
Rufus Willett: Approximate ideal structures and K-theory
Talk by Rufus Willett in Global Noncommutative Geometry Seminar (Americas) http://www.math.wustl.edu/~xtang/NCG-Seminar on May 20, 2020.
From playlist Global Noncommutative Geometry Seminar (Americas)
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