In this video I give an implementation of the power set operation for a crude notion of sets. I then use it to general the hereditarily finite set. I'm motivated both by providing a nice elaboration of a simple model of the ZFC axioms as well as giving a bridge to talk about the AVL-tree d
From playlist Programming
Introduction to Sets and Set Notation
This video defines a set, special sets, and set notation.
From playlist Sets (Discrete Math)
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
Zermelo Fraenkel Pairing and union
This is part of a series of lectures on the Zermelo-Fraenkel axioms for set theory. We discuss the axioms of pairing and union, the two easiest axioms of ZFC, and consider whether they are really needed. For the other lectures in the course see https://www.youtube.com/playlist?list=PL
From playlist Zermelo Fraenkel axioms
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
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
Choiceless Polynomial Time - Ben Rossman
Computer Science/Discrete Mathematics Seminar I Topic: Choiceless Polynomial Time Speaker: Ben Rossman Affiliation: University of Toronto Date: October 14, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
Modern "Set Theory" - is it a religious belief system? | Set Theory Math Foundations 250
Modern pure mathematics suffers from a uniform disinterest in examining the foundations of the subject carefully and objectively. The current belief system that "mathematics is based on set theory" is quite misguided, and in its current form represents an abdication of our responsibility t
From playlist Math Foundations
Bourbaki - 21/03/15 - 2/3 - Sophie GRIVAUX
Espaces de Banach possédant très peu d'opérateurs [d'après S. Argyros et R. Haydon]
From playlist Bourbaki - 21 mars 2015
Basic Methods: We introduce basic notions from naive set theory, including sets, elements, and subsets. We give examples of showing two sets are equal by mutual inclusion. Then we define the power set and note Russell's paradox.
From playlist Math Major Basics
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
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
Bourgain–Delbaen ℒ_∞-spaces and the scalar-plus-compact property – R. Haydon & S. Argyros – ICM2018
Analysis and Operator Algebras Invited Lecture 8.16 Bourgain–Delbaen ℒ_∞-spaces, the scalar-plus-compact property and related problems Richard Haydon & Spiros Argyros Abstract: We outline a general method of constructing ℒ_∞-spaces, based on the ideas of Bourgain and Delbaen, showing how
From playlist Analysis & Operator Algebras
Mathematical Knowledge Management software survey (paper review)
In this video I talk about the paper "The Space of Mathematical Software Systems — A Survey of Paradigmatic Systems" found here: https://arxiv.org/abs/2002.04955 My notes on the text and all links shown on in the video can be found here: https://gist.github.com/Nikolaj-K/87371836d1dd1abfba
From playlist Reviews
This is part of a series of lectures on the Zermelo-Fraenkel axioms for set theory. We discuss the powerset axiom, the strongest of the ZF axioms, and explain why the notion of a powerset is so hard to pin down precisely. For the other lectures in the course see https://www.youtube.com
From playlist Zermelo Fraenkel axioms
This is part of a series of lectures on the Zermelo-Fraenkel axioms for set theory. We discuss the axiom of infinity, and give some examples of models where it does not hold. For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj52EKVgPi-p50fRP2_SbG
From playlist Zermelo Fraenkel axioms
Joseph Huchette: "Neural network verification as piecewise linear optimization"
Deep Learning and Combinatorial Optimization 2021 "Neural network verification as piecewise linear optimization" Joseph Huchette - Rice University Abstract: Neural networks are incredibly powerful tools for prediction in important domains such as image classification and machine translat
From playlist Deep Learning and Combinatorial Optimization 2021
MF150: What exactly is a set? | Data Structures in Mathematics Math Foundations | NJ Wildberger
What exactly is a set?? This is a crucial question in the modern foundations of mathematics. Here we begin an examination of this thorny issue, first by discussing the usual English usage of the term, as well as alternate terms, such as collection, aggregate, bunch, class, menagerie etc th
From playlist Math Foundations
The Realities of Gene Editing with CRISPR I NOVA I PBS
CRISPR gene-editing technology is advancing quickly. What can it do now—and in the future? The revolutionary gene-editing tool known as CRISPR can alter, add, and remove genes from the human genome. The implications are immense: It could help eliminate illnesses like sickle cell disease a
From playlist Original shorts