Partially ordered set

15 Properties of partially ordered sets

When a relation induces a partial ordering of a set, that set has certain properties with respect to the reflexive, (anti)-symmetric, and transitive properties.

From playlist Abstract algebra

Orders on Sets: Part 1 - Partial Orders

This was recorded as supplemental material for Math 115AH at UCLA in the spring quarter of 2020. In this video, I discuss the concept and definition of a partial order.

From playlist Orders on Sets

14 Ordering of sets

The elements of a set can be ordered by a relation. Some relation cause proper ordering and some, partial ordering. Have a look at some examples.

From playlist Abstract algebra

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 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

Set Theory (Part 11): Ordering of the Natural Numbers

Please feel free to leave comments/questions on the video and practice problems below! In this video, we utilize the definition of natural number to speak of ordering on the set of all natural numbers. In addition, the well-ordering principle and trichotomy law are proved.

From playlist Set Theory by Mathoma

BM7. Binary Relations

Note: as noted below, 'equals' is an anti-symmetric relation. But, in practice, intuition for partially ordered sets starts with "less than or equals." Basic Methods: We define the Cartesian product of two sets X and Y and use this to define binary relations on X. We explain the propert

From playlist Math Major Basics

Heaps Of Fun Solution - Intro to Algorithms

This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.

From playlist Introduction to Algorithms

MATH1081 Discrete Maths: Chapter 2 Question 26

Here we look at a question about partially ordered set. We are given a set A consists positive integers, and for two numbers a and b in A, a is related to b if and only if a is a factor of b . Presented by Peter Brown of the School of Mathematics and Statistics, Faculty of Science, UNSW.

From playlist MATH1081 Discrete Mathematics

Orders on Sets: Part 2 - Total Orders

This was recorded as supplemental content for Math 115AH in the spring quarter of 2020. In this video, we investigate in detail a simple example of a poset, and define a new notion: "total order". Hold music: Bossa Antigua by Kevin MacLeod Link: https://incompetech.filmmusic.io/song/3454

From playlist Orders on Sets

What is a Riesz Space? -- MathMajor Seminar

⭐Support the channel⭐ Patreon: https://www.patreon.com/michaelpennmath Merch: https://teespring.com/stores/michael-penn-math My amazon shop: https://www.amazon.com/shop/michaelpenn ⭐my other channels⭐ Main Channel: https://www.youtube.com/michaelpennmath non-math podcast: http

From playlist MathMajor Seminar

The quantum query complexity of sorting under (...) - J. Roland - Main Conference - CEB T3 2017

Jérémie Roland (Brussels) / 15.12.2017 Title: The quantum query complexity of sorting under partial information Abstract: Sorting by comparison is probably one of the most fundamental tasks in algorithmics: given $n$ distinct numbers $x_1,x_2,...,x_n$, the task is to sort them by perfor

From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester

Lec 11 | MIT 6.042J Mathematics for Computer Science, Fall 2010

Lecture 11: Relations, Partial Orders, and Scheduling Instructor: Marten van Dijk View the complete course: http://ocw.mit.edu/6-042JF10 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 6.042J Mathematics for Computer Science, Fall 2010

Zorn's Lemma, The Well-Ordering Theorem, and Undefinability (Version 2.0)

Zorn's Lemma and The Well-ordering Theorem are seemingly straightforward statements, but they give incredibly mind-bending results. Orderings, Hasse Diagrams, and the Ordinals / set theory will come up in this video as tools to get a better view of where the "proof" of Zorn's lemma comes f

From playlist The New CHALKboard

Extremal Combinatorics with Po-Shen Loh 04/01 Wed - 2

Carnegie Mellon University is protecting the community from the COVID-19 pandemic by running courses online for the Spring 2020 semester. This is the video stream for Po-Shen Loh’s PhD-level course 21-738 Extremal Combinatorics. Professor Loh will not be able to respond to questions or com

From playlist CMU PhD-Level Course 21-738 Extremal Combinatorics

2.7.1 Partial Orders: Video

MIT 6.042J Mathematics for Computer Science, Spring 2015 View the complete course: http://ocw.mit.edu/6-042JS15 Instructor: Albert R. Meyer License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 6.042J Mathematics for Computer Science, Spring 2015

2.7.3 Representing Partial Orders As Subset Relations: Video

MIT 6.042J Mathematics for Computer Science, Spring 2015 View the complete course: http://ocw.mit.edu/6-042JS15 Instructor: Albert R. Meyer License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 6.042J Mathematics for Computer Science, Spring 2015

DDPS | Physics-Informed Learning for Nonlinear Dynamical Systems

Talk Abstract Dynamical modeling of a process is essential to study its dynamical behavior and perform engineering studies such as control and optimization. With the ease of accessibility of data, learning models directly from the data have recently drawn much attention. It is also desir

From playlist Data-driven Physical Simulations (DDPS) Seminar Series

Set Theory (Part 5): Functions and the Axiom of Choice

Please feel free to leave comments/questions on the video and practice problems below! In this video, I introduce functions as a special sort of relation, go over some function-related terminology, and also prove two theorems involving left- and right-inverses, with the latter theorem nic

From playlist Set Theory by Mathoma