In the mathematical discipline of set theory, a cardinal characteristic of the continuum is an infinite cardinal number that may consistently lie strictly between (the cardinality of the set of natural numbers), and the cardinality of the continuum, that is, the cardinality of the set of all real numbers. The latter cardinal is denoted or . A variety of such cardinal characteristics arise naturally, and much work has been done in determining what relations between them are provable, and constructing models of set theory for various consistent configurations of them. (Wikipedia).
What is the definition of a ray
👉 Learn essential definitions of points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A plane contains infinite number of lines. A ray is a li
From playlist Points Lines and Planes
👉 Learn essential definitions of points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A plane contains infinite number of lines. A ray is a li
From playlist Points Lines and Planes
👉 Learn essential definitions of points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A plane contains infinite number of lines. A ray is a li
From playlist Points Lines and Planes
👉 Learn essential definitions of points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A plane contains infinite number of lines. A ray is a li
From playlist Points Lines and Planes
👉 Learn essential definitions of points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A plane contains infinite number of lines. A ray is a li
From playlist Points Lines and Planes
Speed of Light - Sixty Symbols
The little "c" representing the speed of light is perhaps the most famous symbol in physics and astronomy. More at http://www.sixtysymbols.com/ Featuring Mike Merrifield and Phil Moriarty.
From playlist Mike Merrifield - Sixty Symbols
Should the power class of any non-empty set even be a set? It's not in constructive Zermelo-Fraenkel, but once you add the Axiom of Choice you end up in ZFC where you have to assign it a cardinal number. But then, well-orderings on something like the reals provably exist that are not descr
From playlist Logic
What is a Ray and how do we label one
👉 Learn essential definitions of points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A plane contains infinite number of lines. A ray is a li
From playlist Points Lines and Planes
Does Infinite Cardinal Arithmetic Resemble Number Theory? - Menachem Kojman
Menachem Kojman Ben-Gurion University of the Negev; Member, School of Mathematics February 28, 2011 I will survey the development of modern infinite cardinal arithmetic, focusing mainly on S. Shelah's algebraic pcf theory, which was developed in the 1990s to provide upper bounds in infinit
From playlist Mathematics
Special Relativity A1 The Postulates of Special Relativity
The postulates of special relativity.
From playlist Physics - Special Relativity
John Roberts: On finding integrals in birational maps
Abstract: At the heart of an integrable discrete map is the existence of a sufficient number of integrals of motion. When the map is birational and the integral is assumed to be a rational function of the variables, many results from algebraic geometry and number theory can be employed in
From playlist Integrable Systems 9th Workshop
The circle and Cartesian coordinates | Universal Hyperbolic Geometry 5 | NJ Wildberger
This video introduces basic facts about points, lines and the unit circle in terms of Cartesian coordinates. A point is an ordered pair of (rational) numbers, a line is a proportion (a:b:c) representing the equation ax+by=c, and the unit circle is x^2+y^2=1. With this notation we determine
From playlist Universal Hyperbolic Geometry
Colloquium MathAlp 2018 - Patrick Dehornoy
La théorie des ensembles cinquante ans après Cohen : On présentera quelques résultats de théorie des ensembles récents, avec un accent sur l'hypothèse du continu et la possibilité de résoudre la question après les résultats négatifs bien connus de Gödel et Cohen, et sur les tables de Lave
From playlist Colloquiums MathAlp
Saharon Shelah : Categoricity of atomic classes in small cardinals, in ZFC
CONFERENCE Recording during the thematic meeting : « Discrete mathematics and logic: between mathematics and the computer science » the January 17, 2023 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Jean Petit Find this video and other talks give
From playlist Logic and Foundations
Fundamentals of Mathematics - Lecture 31: The Power Set of the Naturals, Cardinality Continuum
course page: https://www.uvm.edu/~tdupuy/logic/Math52-Fall2017.html videography - Eric Melton (UVM)
From playlist Fundamentals of Mathematics
Tom Ward - Group automorphisms from a dynamical point of view
PROGRAM: RECENT TRENDS IN ERGODIC THEORY AND DYNAMICAL SYSTEMS DATES: Tuesday 18 Dec, 2012 - Saturday 29 Dec, 2012 VENUE: Department of Mathematics,Faculty of Science, The Maharaja Sayajirao University of Baroda, Vadodara PROGRAM LINK: http://www.icts.res.in/program/ETDS2012 DESCR
From playlist Recent Trends in Ergodic Theory and Dynamical Systems
Infinite Sets and Foundations (Joel David Hamkins) | Ep. 17
Joel David Hamkins is a Professor of Logic with appointments in Philosophy and Mathematics at Oxford University. His main interest is in set theory. We discuss the field of set theory: what it can say about infinite sets and which issues are unresolved, and the relation of set theory to ph
From playlist Daniel Rubin Show, Full episodes
algebraic geometry 30 The Ax Grothendieck theorem
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers the Ax-Grothendieck theorem, which states that an injective regular map between varieties is surjective. The proof uses a strange technique: first prove the resu
From playlist Algebraic geometry I: Varieties
👉 Learn essential definitions of points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A plane contains infinite number of lines. A ray is a li
From playlist Points Lines and Planes
Andre Nies: Randomness connecting to set theory and to reverse mathematics
Abstract : I will discuss two recent interactions of the field called randomness via algorithmic tests. With Yokoyama and Triplett, I study the reverse mathematical strength of two results of analysis. (1) The Jordan decomposition theorem says that every function of bounded variation is th
From playlist Logic and Foundations