In set theory, a branch of mathematics, Kunen's inconsistency theorem, proved by Kenneth Kunen, shows that several plausible large cardinal axioms are inconsistent with the axiom of choice. Some consequences of Kunen's theorem (or its proof) are: * There is no non-trivial elementary embedding of the universe V into itself. In other words, there is no Reinhardt cardinal. * If j is an elementary embedding of the universe V into an inner model M, and λ is the smallest fixed point of j above the critical point κ of j, then M does not contain the set j "λ (the image of j restricted to λ). * There is no ω-huge cardinal. * There is no non-trivial elementary embedding of Vλ+2 into itself. It is not known if Kunen's theorem still holds in ZF (ZFC without the axiom of choice), though showed that there is no definable elementary embedding from V into V. That is there is no formula J in the language of set theory such that for some parameter p∈V for all sets x∈V and y∈V: Kunen used Morse–Kelley set theory in his proof. If the proof is re-written to use ZFC, then one must add the assumption that replacement holds for formulas involving j. Otherwise one could not even show that j "λ exists as a set. The forbidden set j "λ is crucial to the proof. The proof first shows that it cannot be in M. The other parts of the theorem are derived from that. It is possible to have models of set theory that have elementary embeddings into themselves, at least if one assumes some mild large cardinal axioms. For example, if 0# exists then there is an elementary embedding from the constructible universe L into itself. This does not contradict Kunen's theorem because if 0# exists then L cannot be the whole universe of sets. (Wikipedia).
Yuri Kifer: Nonconventional limit theorems in probability and dynamical systems
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Probability and Statistics
Examples of removable and non removable discontinuities to find limits
👉 Learn how to classify the discontinuity of a function. A function is said to be discontinuos if there is a gap in the graph of the function. Some discontinuities are removable while others are non-removable. There is also jump discontinuity. A discontinuity is removable when the denomin
From playlist Holes and Asymptotes of Rational Functions
Learn how to find and classify the discontinuity of the function
👉 Learn how to classify the discontinuity of a function. A function is said to be discontinuous if there is a gap in the graph of the function. Some discontinuities are removable while others are non-removable. There is also jump discontinuity. A discontinuity is removable when the denomi
From playlist Holes and Asymptotes of Rational Functions
Introduction to additive combinatorics lecture 10.8 --- A weak form of Freiman's theorem
In this short video I explain how the proof of Freiman's theorem for subsets of Z differs from the proof given earlier for subsets of F_p^N. The answer is not very much: the main differences are due to the fact that cyclic groups of prime order do not have lots of subgroups, so one has to
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
What are removable and non-removable discontinuties
👉 Learn how to find the removable and non-removable discontinuity of a function. A function is said to be discontinuous at a point when there is a gap in the graph of the function at that point. A discontinuity is said to be removable when there is a factor in the numerator which can cance
From playlist Find the Asymptotes of Rational Functions
How to simplify the difference quotient of a function
👉 Learn how to evaluate the limit of a function using the difference quotient formula. The difference quotient is a measure of the average rate of change of the function over an interval, h. The limit of the difference quotient gives the derivative of the function. The difference quotient
From playlist Evaluate the Limit (PC)
Eddie Chumney in Finland 2012-05-05 PART 3/8
Eddie Chumney is one of the leading Torah teachers in the Hebraic Roots community of Messianic bible-believers today. We had the privilege and honor to have him as a guest in Finland in May 2012, and we organized a few meetings for him to speak in about Hebraic Roots of Christianity. I wil
From playlist Eddie Chumney @ Finland/Suomi @ 2012/5
Fundamentals of Mathematics - Lecture 26: Well-Definedness
course page: https://www.uvm.edu/~tdupuy/logic/Math52-Fall2017.html videography - Eric Melton, UVM
From playlist Fundamentals of Mathematics
What if Current Foundations of Mathematics are Inconsistent? | Vladimir Voevodsky
Vladimir Voevodsky, Professor, School of Mathematics, Institute for Advanced Study http://www.ias.edu/people/faculty-and-emeriti/voevodsky In this lecture, Professor Vladimir Voevodsky begins with Gödel's second incompleteness theorem to discuss the possibility that the formal theory of f
From playlist Mathematics
Math's Existential Crisis (Gödel's Incompleteness Theorems)
Math isn’t perfect, and math can prove it. In this video, we dive into Gödel’s incompleteness theorems, and what they mean for math. Created by: Cory Chang Produced by: Vivian Liu Script Editors: Justin Chen, Brandon Chen, Elaine Chang, Zachary Greenberg Special thanks to Ryan O’Donnell,
From playlist Infinity, and Beyond!
Billy Price and Will Troiani present a series of seminars on foundations of mathematics. In this seminar Billy starts the proof of the completeness theorem. You can join this seminar from anywhere, on any device, at https://www.metauni.org. This video was filmed in Deprecation (https://
From playlist Foundations seminar
Simplifying the difference quotient
👉 Learn how to evaluate the limit of a function using the difference quotient formula. The difference quotient is a measure of the average rate of change of the function over an interval, h. The limit of the difference quotient gives the derivative of the function. The difference quotient
From playlist Evaluate the Limit..........Help!
This is part of a series of lectures on the Zermelo-Fraenkel axioms for set theory. We discuss the axiom of foundation, which says that the membership relation is well founded, and give some examples of the bizarre things that can happen if sets are allowed to be non-well-founded. For
From playlist Zermelo Fraenkel axioms
Learn how to identify the discontinuities as removable or non removable
👉 Learn how to find the removable and non-removable discontinuity of a function. A function is said to be discontinuous at a point when there is a gap in the graph of the function at that point. A discontinuity is said to be removable when there is a factor in the numerator which can cance
From playlist Find the Asymptotes of Rational Functions
Scalable Privacy-Friendly Client Cloud Computing
Carl Hewitt, Emeritus in the Electrical Engineering and Computer Science department at MIT, talks about Organizations of Restricted Generality (ORGs). ORGs is an architecture providing foundations for the development of privacy-friendly Internet applications by incorporating cloud computin
From playlist Engineering
Part2 Week9 2 15oct2021 (Least Squares)
Revision for normal equation and least squares
From playlist Part 2 lectures (2021 zoom)
Gödel's First Incompleteness Theorem, Proof Sketch
Kurt Gödel rocked the mathematical world with his incompleteness theorems. With the halting problems, these proofs are made easy! Created by: Cory Chang Produced by: Vivian Liu Script Editor: Justin Chen Special thanks to Ryan O’Donnell, associate professor at Carnegie Mellon University
From playlist Infinity, and Beyond!
Gödel's Second Incompleteness Theorem, Proof Sketch
In order for math to prove its own correctness, it would have to be incorrect. This result is Gödel’s second incompleteness theorem, and in this video, we provide a sketch of the proof. Created by: Cory Chang Produced by: Vivian Liu Script Editor: Justin Chen, Brandon Chen, Zachary Greenb
From playlist Infinity, and Beyond!
MIT 18.404J Theory of Computation, Fall 2020 Instructor: Michael Sipser View the complete course: https://ocw.mit.edu/18-404JF20 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60_JNv2MmK3wkOt9syvfQWY Quickly reviewed last lecture. Covered NP-completeness; SAT and 3SAT;
From playlist MIT 18.404J Theory of Computation, Fall 2020
Convolution Theorem: Fourier Transforms
Free ebook https://bookboon.com/en/partial-differential-equations-ebook Statement and proof of the convolution theorem for Fourier transforms. Such ideas are very important in the solution of partial differential equations.
From playlist Partial differential equations