Mark Sapir - The Tarski numbers of groups.
Mark Sapir (Vanderbilt University, USA) The Tarski number of a non-amenable group is the minimal number of pieces in a paradoxical decomposition of the group. It is known that a group has Tarski number 4 if and only if it contains a free non-cyclic subgroup, and the Tarski numbers of tors
From playlist T1-2014 : Random walks and asymptopic geometry of groups.
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...
This Math Theorem Proves that 1=1+1 | The Banach-Tarskis Paradox
Mathematicians are in nearly universal agreement that the strangest paradox in math is the Banach-Tarski paradox, in which you can split one ball into a finite number of pieces, then rearrange the pieces to get two balls of the same size. Interestingly, only a minority of mathematicians ha
From playlist Math and Statistics
(ML 11.4) Choosing a decision rule - Bayesian and frequentist
Choosing a decision rule, from Bayesian and frequentist perspectives. To make the problem well-defined from the frequentist perspective, some additional guiding principle is introduced such as unbiasedness, minimax, or invariance.
From playlist Machine Learning
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
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
Video3-4: Existence and Uniqueness Them; Definition of Wronskian. Elementary Differential Equations
Elementary Differential Equations Video3-4: Existence and Uniqueness Theorem; the Definition and applications of Wronskian on linear dependence Course playlist: https://www.youtube.com/playlist?list=PLbxFfU5GKZz0GbSSFMjZQyZtCq-0ol_jD
From playlist Elementary Differential Equations
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
Kurt Gödel Centenary - Part III
John W. Dawson, Jr. Pennsylvania State University November 17, 2006 More videos on http://video.ias.edu
From playlist Kurt Gödel Centenary
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
Measurable equidecompositions – András Máthé – ICM2018
Analysis and Operator Algebras Invited Lecture 8.8 Measurable equidecompositions András Máthé Abstract: The famous Banach–Tarski paradox and Hilbert’s third problem are part of story of paradoxical equidecompositions and invariant finitely additive measures. We review some of the classic
From playlist Analysis & Operator Algebras
Matthew Foreman: Welch games to Laver ideals
Recorded during the meeting "XVI International Luminy Workshop in Set Theory" the September 16, 2021 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 Au
From playlist Logic and Foundations
The Mathematical Truth | Enrico Bombieri
Enrico Bombieri, Professor Emeritus, School of Mathematics, Institute for Advanced Study http://www.ias.edu/people/faculty-and-emeriti/bombieri October 29, 2010 In this lecture, Professor Enrico Bombieri attempts to give an idea of the numerous different notions of truth in mathematics.
From playlist Mathematics
(ML 11.8) Bayesian decision theory
Choosing an optimal decision rule under a Bayesian model. An informal discussion of Bayes rules, generalized Bayes rules, and the complete class theorems.
From playlist Machine Learning
How the Axiom of Choice Gives Sizeless Sets | Infinite Series
Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi Does every set - or collection of numbers - have a size: a length or a width? In other words, is it possible for a set to be sizeless? This in an updated version of our
From playlist An Infinite Playlist
How to Determine if Functions are Linearly Independent or Dependent using the Definition
How to Determine if Functions are Linearly Independent or Dependent using the Definition If you enjoyed this video please consider liking, sharing, and subscribing. You can also help support my channel by becoming a member https://www.youtube.com/channel/UCr7lmzIk63PZnBw3bezl-Mg/join Th
From playlist Zill DE 4.1 Preliminary Theory - Linear Equations
Infinity shapeshifter vs. Banach-Tarski paradox
Take on solid ball, cut it into a couple of pieces and rearrange those pieces back together into two solid balls of exactly the same size as the original ball. Impossible? Not in mathematics! Recently Vsauce did a brilliant video on this so-called Banach-Tarski paradox: https://youtu.be/s
From playlist Recent videos