Well-Ordering and Induction: Part 1
This was recorded as supplemental material for Math 115AH at UCLA in the spring quarter of 2020. In this video, I prove the equivalence of the principle of mathematical induction and the well-ordering principle.
From playlist Well Ordering and Induction
Discrete Math - 5.2.1 The Well-Ordering Principle and Strong Induction
In this video we introduce the well-ordering principle and look and one proof by strong induction. Textbook: Rosen, Discrete Mathematics and Its Applications, 7e Playlist: https://www.youtube.com/playlist?list=PLl-gb0E4MII28GykmtuBXNUNoej-vY5Rz
From playlist Discrete Math I (Entire Course)
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
1.3.1 Well Ordering Principle 1: 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
Well-ordering Principle and Division Algorithm || Polynomial Prerequisites || Intermediate Algebra
Here I have already diverted from the standard Principle as the Well-ordering Principle usually goes with the Natural Numbers (ℕ) and the Division Algorithm over the Integers (ℤ). Here's some more nice content. Well-ordering Principle: 1. https://en.wikipedia.org/wiki/Well-ordering_princi
From playlist Summer of Math Exposition 2 videos
Well Ordering and Induction: Part 2
This was recorded as supplemental material for Math 115AH at UCLA in the spring quarter of 2020. In this video, I discuss the "philosophical importance" of induction, and go over two proofs that use the Principle of Mathematical Induction and the Well-Ordering Principle, respectively.
From playlist Well Ordering and Induction
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
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 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
A positive proportion of plane cubics fail the Hasse principle - Manjul Bhargava [2011]
Arithmetic Statistics April 11, 2011 - April 15, 2011 April 11, 2011 (02:10 PM PDT - 03:00 PM PDT) Speaker(s): Manjul Bhargava (Princeton University) Location: MSRI: Simons Auditorium http://www.msri.org/workshops/567/schedules/12761
From playlist Number Theory
Joel David Hamkins : The hierarchy of second-order set theories between GBC and KM and beyond
Abstract: Recent work has clarified how various natural second-order set-theoretic principles, such as those concerned with class forcing or with proper class games, fit into a new robust hierarchy of second-order set theories between Gödel-Bernays GBC set theory and Kelley-Morse KM set th
From playlist Logic and Foundations
Dylan Possamaï: Principal Agent Modelling - lecture 1
CIRM HYBRID EVENT These lectures will consist in an overview of recent progresses made in contracting theory, using the so-called dynamic programming approach. The basic situation is that of a Principal wanting to hire an Agent to do a task on his behalf, and who has to be properly incenti
From playlist Probability and Statistics
Real Analysis Lecture 1.1 The Natural Numbers
00:00 Start 00:11 Overview 01:38 Natural Numbers 08:00 A Joke 12:02 Tiling By Trominos 33:41 Integers Full Playlist: https://www.youtube.com/playlist?list=PLX2fVLMrzfneCYOpe6UrBhhFDo3JNglke Suggestion: Play at 1.25 times the normal speed. Note: The auto-generated subtitles are mostly acc
From playlist Summer of Math Exposition Youtube Videos
LA Ruby Conf 2014 - SOLID principles through tests by Sebastian Sogamoso
We care about writing quality code, we have read the definition of SOLID principles several times and we know how important they are for writing good OO code, but are we really following those principles? Is there a pragmatic way of following them in our day to day jobs or are they just so
From playlist LA RubyConf 2014
No Cause for Concern: Indefinite Causal Ordering / Tool for Understanding Entanglement: Conversation
Moderated Conversation with Yemima Ben-Menahem, Department of Philosophy, The Hebrew University of Jerusalem and Professor Elise Crull. Understanding the sorts of explanations and inferences that causal processes countenance is of course of great interest to philosophers and physicists (am
From playlist Franke Program in Science and the Humanities
Ronald Dworkin Interview on the Constitution (1987)
Ronald Dworkin discusses the meaning of the Constitution in an interview with Bill Moyers back in 1987. 00:00 Introduction 00:52 Meet Ronald Dworkin 03:34 British vs American Constitution 08:32 An Ongoing Story 12:25 Original Intent 17:24 Principle of Constitution 18:30 Rights 21:55 AIDS
From playlist Social & Political Philosophy
Graph Theory: 15.There Exists a 3-Regular Graph of All Even Order at least 4
This video is an example of a proof by induction. I begin by explaining the Principle of Mathematical Induction and then use this technique to prove that for every even integer n which is at least 4, there exists a 3-regular graph of that order. --An introduction to Graph Theory by Dr. Sa
From playlist Graph Theory part-3
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