In mathematics, subtle cardinals and ethereal cardinals are closely related kinds of large cardinal number. A cardinal κ is called subtle if for every closed and unbounded C ⊂ κ and for every sequence A of length κ for which element number δ (for an arbitrary δ), Aδ ⊂ δ, there exist α, β, belonging to C, with α < β, such that Aα = Aβ ∩ α. A cardinal κ is called ethereal if for every closed and unbounded C ⊂ κ and for every sequence A of length κ for which element number δ (for an arbitrary δ), Aδ ⊂ δ and Aδ has the same cardinal as δ, there exist α, β, belonging to C, with α < β, such that card(α) = card(Aβ ∩ Aα). Subtle cardinals were introduced by . Ethereal cardinals were introduced by . Any subtle cardinal is ethereal, and any strongly inaccessible ethereal cardinal is subtle. (Wikipedia).
Art is for everyone! What is BAROQUE?
A quick definition of Baroque. Art Lover: Louise McCartney Director: Michael Harrison Written and Produced by Kimberly Hatch Harrison ♦♦♦♦♦♦♦♦♦♦ Ways to support our channel: ► Join our Patreon : https://www.patreon.com/socratica ► Make a one-time PayPal donation: https://www.paypal.m
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Gradient (2 of 3: Angle of inclination)
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What are the Angle Relationships for Parallel Lines and a Transversal
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Statistics for Families of Automorphic Representations - Sug-Woo Shin
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Determine the values of two angles that lie on a lie with a third angle
👉 Learn how to define and classify different angles based on their characteristics and relationships are given a diagram. The different types of angles that we will discuss will be acute, obtuse, right, adjacent, vertical, supplementary, complementary, and linear pair. The relationships
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How Big are All Infinities Combined? (Cantor's Paradox) | Infinite Series
Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi Infinities come in different sizes. There’s a whole tower of progressively larger "sizes of infinity". So what’s the right way to describe the size of the whole tower?
From playlist An Infinite Playlist
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Harald Helfgott - 2/4 Growth in groups and applications
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From playlist École d'été 2014 - Théorie analytique des nombres
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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
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The Green - Tao Theorem (Lecture 6) by D. S. Ramana
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H.Chen - Théorème de Hilbert-Samuel arithmétique (Part3)
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From playlist Ecole d'été 2017 - Géométrie d'Arakelov et applications diophantiennes
A new basis theorem for ∑13 sets
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Chandrashekhar Khare: Automorphy lifting via level lowering congruences
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From playlist Algebraic and Complex Geometry
The Green - Tao Theorem (Lecture 8) by D. S. Ramana
Program Workshop on Additive Combinatorics ORGANIZERS: S. D. Adhikari and D. S. Ramana DATE: 24 February 2020 to 06 March 2020 VENUE: Madhava Lecture Hall, ICTS Bangalore Additive combinatorics is an active branch of mathematics that interfaces with combinatorics, number theory, ergod
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Lecture 2: Cantor's Theory of Cardinality (Size)
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From playlist MIT 18.100A Real Analysis, Fall 2020