What are Vertex Separating Sets? | Graph Theory
What are vertex separating sets in graph theory? We'll be going over the definition of a vertex separating set and some examples in today's video graph theory lesson! Let G be a graph and S be a vertex cut of G. As in, S is a set of vertices of G such that G - S is disconnected. Then, let
From playlist Set Theory
Introduction to Sets and Set Notation
This video defines a set, special sets, and set notation.
From playlist Sets (Discrete Math)
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
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
9.3.1 Sets: Definitions and Notation
9.3.1 Sets: Definitions and Notation
From playlist LAFF - Week 9
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
Partitions of a Set | Set Theory
What is a partition of a set? Partitions are very useful in many different areas of mathematics, so it's an important concept to understand. We'll define partitions of sets and give examples in today's lesson! A partition of a set is basically a way of splitting a set completely into disj
From playlist Set Theory
Proof: Menger's Theorem | Graph Theory, Connectivity
We prove Menger's theorem stating that for two nonadjacent vertices u and v, the minimum number of vertices in a u-v separating set is equal to the maximum number of internally disjoint u-v paths. If you want to learn about the theorem, see how it relates to vertex connectivity, and see
From playlist Graph 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
What is a Manifold? Lesson 3: Separation
He we present some alternative topologies of a line interval and then discuss the notion of separability. Note the error at 4:05. Sorry! If you are viewing this on a mobile device, my annotations are not visible. This is due to a quirck of YouTube.
From playlist What is a Manifold?
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
Kazuo Murota: Discrete Convex Analysis (Part 3)
The lecture was held within the framework of the Hausdorff Trimester Program: Combinatorial Optimization
From playlist HIM Lectures 2015
Intro to Menger's Theorem | Graph Theory, Connectivity
Menger's theorem tells us that for any two nonadjacent vertices, u and v, in a graph G, the minimum number of vertices in a u-v separating set is equal to the maximum number of internally disjoint u-v paths in G. The Proof of Menger's Theorem: https://youtu.be/2rbbq-Mk-YE Remember that
From playlist Graph Theory
38th Annual Geometric Topology Workshop (Online), June 15-17, 2021 Eric Swenson, Brigham Young University Title: Cuts and blobs Abstract: We provide sharp conditions under which a collection of separators of a connected topological space leads to a canonical -tree . Any group acting on
From playlist 38th Annual Geometric Topology Workshop (Online), June 15-17, 2021
Zermelo Fraenkel Separation and replacement
This is part of a series of lectures on the Zermelo-Fraenkel axioms for set theory. We discuss the axioms of separation and replacement and some of their variations. For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj52EKVgPi-p50fRP2_SbG2oi
From playlist Zermelo Fraenkel axioms
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
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
Schemes 21: Separated morphisms
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne.. We define separated and quasi-separated schemes and morphisms, give a few examples, and show that if a scheme has a separated morphism to an affine scheme the
From playlist Algebraic geometry II: Schemes