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 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
This lecture is part of an online course on the Zermelo Fraenkel axioms of set theory. This lecture gives an overview of the axioms, describes the von Neumann hierarchy, and sketches several approaches to interpreting the axioms (Platonism, von Neumann hierarchy, multiverse, formalism, pra
From playlist Zermelo Fraenkel axioms
This video lists an explains propositional, predicate calculus axioms, as well as a set theoretical statement that goes with it, including ZF and beyond. Where possible, the explanations are kept constructive. You can find the list of axioms in the file discussed in this video here: https:
From playlist Logic
Theory of numbers: Gauss's lemma
This lecture is part of an online undergraduate course on the theory of numbers. We describe Gauss's lemma which gives a useful criterion for whether a number n is a quadratic residue of a prime p. We work it out explicitly for n = -1, 2 and 3, and as an application prove some cases of Di
From playlist Theory of numbers
The Big (mathematical) Bang | Axiomatic Set Theory, Section 0
The introductory video for a course on the axiomatic theory of ZFC set theory. My Twitter: https://twitter.com/KristapsBalodi3 Intro: (0:00) Russel's Paradox: (2:13)
From playlist Axiomatic Set Theory
The Definition of a Linear Equation in Two Variables
This video defines a linear equation in to variables and provides examples of the different forms of linear equations. http://mathispower4u.com
From playlist The Coordinate Plane, Plotting Points, and Solutions to Linear Equations in Two Variables
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
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
Fundamentals of Mathematics - Lecture 15: Dedekind-Peano vs Peano Arithmetic
This is the class where we talk about the Extra Credit. course page: http://www.uvm.edu/~tdupuy/logic/Math52-Fall2017.html videography - Eric Melton - UVM
From playlist Fundamentals of Mathematics
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
Topology Without Tears - Video 2c - Infinite Set Theory
This is the final part, part (c), of Video 2 in a series of videos supplementing the online book "Topology Without Tears" which is available at no cost at www.topologywithouttears.net
From playlist Topology Without Tears
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
What We've Learned from NKS Chapter 12: The Principle of Computational Equivalence [Part 2]
In this episode of "What We've Learned from NKS", Stephen Wolfram is counting down to the 20th anniversary of A New Kind of Science with [another] chapter retrospective. If you'd like to contribute to the discussion in future episodes, you can participate through this YouTube channel or th
From playlist Science and Research Livestreams
Peano axioms: Can you really PROVE that 2+2=4?
How do you prove 2 + 2 = 4? I mean, it's just TRUE right? If you think this, well, Mr. Peano would like to have a word with you. Natural number game: https://www.ma.imperial.ac.uk/~buzzard/xena/natural_number_game/ This video was made for 3Blue1Brown's SoME1 competition.
From playlist Summer of Math Exposition Youtube Videos
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
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
In this video I write down the axioms of Lie algebras and then discuss the defining anti-symmetric bilinear map (the Lie bracket) which is zero on the diagonal and fulfills the Jacobi identity. I'm following the compact book "Introduction to Lie Algebras" by Erdmann and Wildon. https://gi
From playlist Algebra