What's so wrong with the Axiom of Choice ?
One of the Zermelo- Fraenkel axioms, called axiom of choice, is remarkably controversial. It links to linear algebra and several paradoxes- find out what is so strange about it ! (00:22) - Math objects as sets (00:54) - What axioms we use ? (01:30) - Understanding axiom of choice (03:2
From playlist Something you did not know...
The Axiom of Choice | Epic Math Time
The axiom of choice states that the cartesian product of nonempty sets is nonempty. This doesn't sound controversial, and it might not even sound interesting, but adopting the axiom of choice has far reaching consequences in mathematics, and applying it in proofs has a very distinctive qua
From playlist Latest Uploads
Choice Functions and Length: Why you can't measure everything you choose
I haven't talked about the axiom of choice in a while, and the relationship between choice functions and length (or size) and why you can't measure everything you choose seemed like a good way to do so. The interplay between choice functions and how one can construct sets for which measure
From playlist The New CHALKboard
This is part of a series of lectures on the Zermelo-Fraenkel axioms for set theory. We dicuss the axiom of chice, and sketch why it is independent of the other axioms of set theory. For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj52EKVgPi-p50f
From playlist Zermelo Fraenkel axioms
Determine Infinite Limits of a Rational Function Using a Table and Graph (Squared Denominator)
This video explains how to determine a limits and one-sided limits. The results are verified using a table and a graph.
From playlist Infinite Limits
Difficulties with real numbers as infinite decimals ( I) | Real numbers + limits Math Foundations 91
There are three quite different approaches to the idea of a real number as an infinite decimal. In this lecture we look carefully at the first and most popular idea: that an infinite decimal can be defined in terms of an infinite sequence of digits appearing to the right of a decimal point
From playlist Math Foundations
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
Math 101 091317 Introduction to Analysis 06 Introduction to the Least Upper Bound Axiom
Definition of the maximum (minimum) of a set. Existence of maximum and minimum for finite sets. Definitions: upper bound of a set; bounded above; lower bound; bounded below; bounded. Supremum (least upper bound); infimum (greatest lower bound). Statement of Least Upper Bound Axiom (com
From playlist Course 6: Introduction to Analysis (Fall 2017)
Fundamentals of Mathematics - Lecture 33: Dedekind's Definition of Infinite Sets are FInite Sets
https://www.uvm.edu/~tdupuy/logic/Math52-Fall2017.html
From playlist Fundamentals of Mathematics
Real Analysis: Noting that we assume only naive set theory and basic properties of the natural numbers for this playlist, we give a brief account of some issues in the quest for mathematical rigor. These include the Axiom of Choice, the Law of the Excluded Middle, and Godel's Incompleten
From playlist Real Analysis
Wolfram Physics Project: Working Session Tuesday, July 28, 2020 [Metamathematics | Part 3]
This is a Wolfram Physics Project progress update at the Wolfram Summer School. This is a continuation of part two found here: https://youtu.be/ndtLa0BhEdg Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this project by visiting our website: http://wolfr.
From playlist Wolfram Physics Project Livestream Archive
Foundations S2 - Seminar 3 - Skolemisation
A seminar series on the foundations of mathematics, by Will Troiani and Billy Snikkers. This season the focus is on the proof of the Ax-Grothendieck theorem: an injective polynomial function from affine space (over the complex numbers) to itself is surjective. This week Will started into t
From playlist Foundations seminar
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
Egbert Rijke: Daily applications of the univalence axiom - lecture 1
HYBRID EVENT Recorded during the meeting "Logic and Interactions" the February 21, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual M
From playlist Combinatorics
Death by infinity puzzles and the Axiom of Choice
In this video the Mathologer sets out to commit the perfect murder using infinitely many assassins and, subsequently, to get them off the hook in court. The story is broken up into three very tricky puzzles. Challenge yourself to figure them out before the Mathologer reveals his own soluti
From playlist Recent videos
Séminaire Bourbaki - 21/06/2014 - 3/4 - Thomas C. HALES
Developments in formal proofs A for mal proof is a proof that can be read and verified by computer, directly from the fundamental rules of logic and the foundational axioms of mathematics. The technology behind for mal proofs has been under development for decades and grew out of efforts i
From playlist Bourbaki - 21 juin 2014
At the end, I misspoke: the correct statement would be that the axiom of choice (or the choice function) is not constructive.
From playlist Abstract Algebra 1
The Simplest Math No One Can Agree on- A Paradox of Choice
To build our mathematics we need a starting point, rules to dictate what we can do and assumed basic truths to serve as a foundation as we seek understanding of higher level problems. But what happens when we can't agree on what we should start with?
From playlist Summer of Math Exposition Youtube Videos