In mathematics, the category Ord has preordered sets as objects and order-preserving functions as morphisms. This is a category because the composition of two order-preserving functions is order preserving and the identity map is order preserving. The monomorphisms in Ord are the injective order-preserving functions. The empty set (considered as a preordered set) is the initial object of Ord, and the terminal objects are precisely the singleton preordered sets. There are thus no zero objects in Ord. The categorical product in Ord is given by the product order on the cartesian product. We have a forgetful functor Ord → Set that assigns to each preordered set the underlying set, and to each order-preserving function the underlying function. This functor is faithful, and therefore Ord is a concrete category. This functor has a left adjoint (sending every set to that set equipped with the equality relation) and a right adjoint (sending every set to that set equipped with the total relation). (Wikipedia).
Introduction to Sets and Set Notation
This video defines a set, special sets, and set notation.
From playlist Sets (Discrete Math)
Sets Basics - Introduction | Don't Memorise
After we define what Sets are, we will see where Sets are used in daily life! We will also look at the different types of sets like Finite Sets, Infinite Sets, Singleton Sets, Empty Sets, Equivalent Sets, Equal Sets, Subsets, Null sets and Universal sets. We will also understand how Sets
From playlist Middle School Math - Sets
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
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
Category Theory 3.1: Examples of categories, orders, monoids
Examples of categories, orders, monoids.
From playlist Category 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
9.3.1 Sets: Definitions and Notation
9.3.1 Sets: Definitions and Notation
From playlist LAFF - Week 9
Riccardo Zanfa - Extending the topological presheaf-bundle adjunction to sites and toposes
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/ZanfaSlidesToposesOnline.pdf Riccardo Zanfa: “Extending the topological presheaf-bundle adjunction to sites and topo
From playlist Toposes online
Set Theory 1.4 : Well Orders, Order Isomorphisms, and Ordinals
In this video, I introduce well ordered sets and order isomorphisms, as well as segments. I use these new ideas to prove that all well ordered sets are order isomorphic to some ordinal. Email : fematikaqna@gmail.com Discord: https://discord.gg/ePatnjV Subreddit : https://www.reddit.com/r/
From playlist Set Theory
Jacob Leygonie (6/1/20): Differential calculus on persistence barcodes
Title: Differential calculus on persistence barcodes Abstract: We define notions of differentiability for maps from and to the space of persistence barcodes. Inspired by the theory of diffeological spaces, the proposed framework uses lifts to the space of ordered barcodes, from which deri
From playlist ATMCS/AATRN 2020
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
Supercuspidal representations of GL(n) over a... (Lecture 3) by Vincent Sécherre
PROGRAM : ALGEBRAIC AND ANALYTIC ASPECTS OF AUTOMORPHIC FORMS ORGANIZERS : Anilatmaja Aryasomayajula, Venketasubramanian C G, Jurg Kramer, Dipendra Prasad, Anandavardhanan U. K. and Anna von Pippich DATE & TIME : 25 February 2019 to 07 March 2019 VENUE : Madhava Lecture Hall, ICTS Banga
From playlist Algebraic and Analytic Aspects of Automorphic Forms 2019
Category Theory 1.2 : Examples of Categories and Clarification
In this video, I clarify some terminology, and show some very important examples of categories. This includes the category of groups, sets, topologic spaces, monoids, modules, and rings. I also discuss the relation between categories and individual groups, preorders, matrices, and ordinals
From playlist Category Theory
Excel Magic Trick 654: Charts: Line & X Y Scatter
Download Files: https://people.highline.edu/mgirvin/YouTubeExcelIsFun/EMT648-660.xlsx Learn when to use the Line chart and when to use an X-Y Scatter diagram. See the difference between the Line and the X-Y Scatter diagram Charts. Line is for 1 number and a label. X-Y Scatter diagram is f
From playlist Excel Series: Magic Tricks (4th 200 videos)
Stanford Lecture: Donald Knuth - "Bayesian trees and BDDs" (2011)
December 8th, 2011 Professor Donald Knuth's 17th annual Christmas Tree Lecture. Knuth explains how to apply elementary BDD technology so that the probability of such events (and many others) can be computed in polynomial time. Learn more: http://scpd.stanford.edu/knuth/index.jsp
From playlist Donald Knuth Lectures
Binary Tree 3. Traverse (algorithms, pseudocode and VB.NET code)
This is the third in a series of videos about binary trees. It explains the differences between three depth first traversal strategies, namely pre order, in order and post order. It illustrates a simple method for determining the order in which data will be retrieved by each of these dept
From playlist Data Structures
The Hurricane Category Scale Is Broken
Offset your carbon footprint with Wren! They'll plant 10 extra trees for each of the first 100 people who sign up at https://www.wren.co/start/minuteearth. The current hurricane category scale doesn’t accurately convey the danger of a storm, because it doesn’t account for a hurricane's mos
From playlist MinuteEarth
The Most Mindblowing Infrastructure in My City
I wrote a book! And to celebrate, I went around San Antonio filming a few of my favorite infrastructure projects. Check out all the preorder locations here: https://practical.engineering/book Want a free signed copy? Make a social media post with the hashtag #EngineeringInPlainSight. I'll
From playlist Civil Engineering
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