In set theory, a projection is one of two closely related types of functions or operations, namely: * A set-theoretic operation typified by the jth projection map, written , that takes an element of the Cartesian product to the value . * A function that sends an element x to its equivalence class under a specified equivalence relation E, or, equivalently, a surjection from a set to another set. The function from elements to equivalence classes is a surjection, and every surjection corresponds to an equivalence relation under which two elements are equivalent when they have the same image. The result of the mapping is written as [x] when E is understood, or written as [x]E when it is necessary to make E explicit. (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
Set Theory (Part 3): Ordered Pairs and Cartesian Products
Please feel free to leave comments/questions on the video and practice problems below! In this video, I cover the Kuratowski definition of ordered pairs in terms of sets. This will allow us to speak of relations and functions in terms of sets as the basic mathematical objects and will ser
From playlist Set Theory by Mathoma
Set Theory (Part 1): Notation and Operations
Please feel free to leave comments/questions on the video and practice problems below! In this video series, we'll explore the basics of set theory. I assume no experience with set theory in the video series and anyone who's "been around town" in math should understand the videos. To make
From playlist Set Theory by Mathoma
Listing Subsets Using Tree Diagrams | Set Theory, Subsets, Power Sets
Here is a method for completely listing the subsets of a given set using tree diagrams. It's a handy way to make sure you don't miss any subsets when trying to find them. It's not super efficient, but it is reliable! The process is pretty simple, we begin with the empty set, and then branc
From playlist Set Theory
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
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
New Results on Projections - Guy Moshkovitz
Computer Science/Discrete Mathematics Seminar II Topic: New Results on Projections Speaker: Guy Moshkovitz Affiliation: Member, School of Mathematics Date: January 22, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
A new basis theorem for ∑13 sets
Distinguished Visitor Lecture Series A new basis theorem for ∑13 sets W. Hugh Woodin Harvard University, USA and University of California, Berkeley, USA
From playlist Distinguished Visitors Lecture Series
Connecting tropical intersection theory with polytope algebra in types A and B by Alex Fink
PROGRAM COMBINATORIAL ALGEBRAIC GEOMETRY: TROPICAL AND REAL (HYBRID) ORGANIZERS Arvind Ayyer (IISc, India), Madhusudan Manjunath (IITB, India) and Pranav Pandit (ICTS-TIFR, India) DATE & TIME: 27 June 2022 to 08 July 2022 VENUE: Madhava Lecture Hall and Online Algebraic geometry is t
From playlist Combinatorial Algebraic Geometry: Tropical and Real (HYBRID)
Colloquium MathAlp 2018 - Patrick Dehornoy
La théorie des ensembles cinquante ans après Cohen : On présentera quelques résultats de théorie des ensembles récents, avec un accent sur l'hypothèse du continu et la possibilité de résoudre la question après les résultats négatifs bien connus de Gödel et Cohen, et sur les tables de Lave
From playlist Colloquiums MathAlp
Modular theory and QFT (Lecture 1) by Nima Lashkari
Infosys-ICTS String Theory Lectures Modular theory and QFT Speaker: Nima Lashkari (Purdue University) Date: 03 February 2020 to 05 February 2020 Venue: Emmy Noether ICTS-TIFR, Bengaluru Lecture 1: Monday, 3 February 2020 at 11:30 am Lecture 2: Tuesday, 4 February 2020 at 11:30 am Le
From playlist Infosys-ICTS String Theory Lectures
Stability of the set of quantum states - S. Weis - Workshop 2 - CEB T3 2017
Stephan Weis / 26.10.17 Stability of the set of quantum states A convex set C is stable if the midpoint map (x,y) - (x+y)/2 is open. For compact C the Vesterstrøm–O’Brien theorem asserts that C is stable if and only if the barycentric map from the set of all Borel probability measures to
From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester
Yonatan Harpaz - New perspectives in hermitian K-theory I
For questions and discussions of the lecture please go to our discussion forum: https://www.uni-muenster.de/TopologyQA/index.php?qa=k%26l-conference This lecture is part of the event "New perspectives on K- and L-theory", 21-25 September 2020, hosted by Mathematics Münster: https://go.wwu
From playlist New perspectives on K- and L-theory
Adam Topaz - The Liquid Tensor Experiment - IPAM at UCLA
Recorded 13 February 2023. Adam Topaz of the University of Alberta presents "The Liquid Tensor Experiment" at IPAM's Machine Assisted Proofs Workshop. Learn more online at: http://www.ipam.ucla.edu/programs/workshops/machine-assisted-proofs/
From playlist 2023 Machine Assisted Proofs Workshop
What is the Cartesian Product of Sets? | Set Theory
What is the Cartesian product of two sets? The Cartesian product can be generalized to more than two sets, but in this video we go over Cartesian products of two sets! Here is how it works. If you have two sets, A and B, then their Cartesian product, written A x B, is the set containing al
From playlist Set Theory
Charles Weibel: K-theory of algebraic varieties (Lecture 2)
The lecture was held within the framework of the Hausdorff Trimester Program: K-Theory and Related Fields. Charles Weibel: K theory of algebraic varieties Abstract: Lecture 1 will present definitions for the Waldhausen K-theory of rings, varieties, additive and exact categories, and dg c
From playlist HIM Lectures: Trimester Program "K-Theory and Related Fields"