Determinacy | Axioms of set theory
In mathematics, the axiom of real determinacy (abbreviated as ADR) is an axiom in set theory. It states the following: Axiom — Consider infinite two-person games with perfect information. Then, every game of length ω where both players choose real numbers is determined, i.e., one of the two players has a winning strategy. The axiom of real determinacy is a stronger version of the axiom of determinacy (AD), which makes the same statement about games where both players choose integers; ADR is inconsistent with the axiom of choice. It also implies the existence of inner models with certain large cardinals. ADR is equivalent to AD plus the axiom of uniformization. (Wikipedia).
Ex: Determinant of a 2x2 Matrix
This video provides two examples of calculating a 2x2 determinant. One example contains fractions. Site: http://mathispower4u.com
From playlist The Determinant of a Matrix
Gabriel Goldberg: The Jackson analysis and the strongest hypotheses
HYBRID EVENT Recorded during the meeting "XVI International Luminy Workshop in Set Theory" the September 13, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematician
From playlist Logic and Foundations
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
Linear Algebra: Ch 2 - Determinants (1 of 48) What is a Determinant? (Part 1)
Visit http://ilectureonline.com for more math and science lectures! In this video I will give a general definition of “What is a Determinant?” (Part 1) Next video in this series can be seen at: https://youtu.be/vIHnlNjRnGU
From playlist LINEAR ALGEBRA 2: DETERMINANTS
Counting Woodin cardinals in HOD
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From playlist Distinguished Visitors Lecture Series
Distinguished Visitor Lecture Series Finding randomness Theodore A. Slaman University of California, Berkeley, USA
From playlist Distinguished Visitors Lecture Series
Set Theory - What is Set Theory and what is it for? Oxford Mathematics 3rd Year Student Lecture
This is the first of four lectures from Robin Knight's 3rd Year Set Theory course. Robin writes: "Infinity baffled mathematicians, and everyone else, for thousands of years. But around 1870, Georg Cantor worked out how to study infinity in a way that made sense, and created set theory. Mo
From playlist Oxford Mathematics Student Lectures - Set Theory
(3.2.3) The Determinant of Square Matrices and Properties
This video defines the determinant of a matrix and explains what a determinant means in terms of mapping and area. https://mathispower4u.com
From playlist Differential Equations: Complete Set of Course Videos
Ordered Fields In this video, I define the notion of an order (or inequality) and then define the concept of an ordered field, and use this to give a definition of R using axioms. Actual Construction of R (with cuts): https://youtu.be/ZWRnZhYv0G0 COOL Construction of R (with sequences)
From playlist Real Numbers
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Determinant of an operator. An operator is not invertible if and only if its determinant equals 0. Formula for the characteristic polynomial in terms of determinants. Determinant of a matrix. Connection between the two notions of determinant.
From playlist Linear Algebra Done Right
Robert Pippin - Radical Finitude in the Anti-Idealist Modern European Philosophical Tradition”
Robert Pippin is Evelyn Stefansson Nef Distinguished Service Professor in the Committee on Social Thought, the Department of Philosophy, and the College at the University of Chicago. He is the author of Kant’s Theory of Form; Hegel’s Idealism: The Satisfactions of Self-Consciousness; Moder
From playlist Franke Lectures in the Humanities
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We prove the natural ordering on the natural numbers is a total order. Transitivity (0:00) Asymmetry (6:02) All elements are comparable (8:45)
From playlist Axiomatic Set Theory
Ralf Schindler Universität Münster, Germany
From playlist Talks of Mathematics Münster's reseachers
Characterization of the determinant
In this video, I show why the determinant is so special in math: Namely, it is the only function which is multilinear, alternating, and has the value 1 at the identity matrix. This is a generalization of a previous matrix puzzle for the 2 x 2 case. 2 x 2 case: https://youtu.be/lIMeIC1ZJO8
From playlist Determinants
16. Nondeterministic Parallel Programming
MIT 6.172 Performance Engineering of Software Systems, Fall 2018 Instructor: Charles Leiserson View the complete course: https://ocw.mit.edu/6-172F18 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63VIBQVWguXxZZi0566y7Wf Prof. Leiserson discusses nondeterministic paral
From playlist MIT 6.172 Performance Engineering of Software Systems, Fall 2018
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
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From playlist Distinguished Visitors Lecture Series