Order theory

Laver's theorem

Laver's theorem, in order theory, states that order embeddability of countable total orders is a well-quasi-ordering. That is, for every infinite sequence of totally-ordered countable sets, there exists an order embedding from an earlier member of the sequence to a later member. This result was previously known as Fraïssé's conjecture, after Roland Fraïssé, who conjectured it in 1948; Richard Laver proved the conjecture in 1971. More generally, Laver proved the same result for order embeddings of countable unions of scattered orders. In reverse mathematics, the version of the theorem for countable orders is denoted FRA (for Fraïssé) and the version for countable unions of scattered orders is denoted LAV (for Laver). In terms of the "big five" systems of second-order arithmetic, FRA is known to fall in strength somewhere between the strongest two systems, -CA0 and ATR0, and to be weaker than -CA0. However, it remains open whether it is equivalent to ATR0 or strictly between these two systems in strength. (Wikipedia).

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Lagrange theorem

We finally get to Lagrange's theorem for finite groups. If this is the first video you see, rather start at https://www.youtube.com/watch?v=F7OgJi6o9po&t=6s In this video I show you how the set that makes up a group can be partitioned by a subgroup and its cosets. I also take a look at

From playlist Abstract algebra

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Proof of Lemma and Lagrange's Theorem

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Proof of Lemma and Lagrange's Theorem. This video starts by proving that any two right cosets have the same cardinality. Then we prove Lagrange's Theorem which says that if H is a subgroup of a finite group G then the order of H div

From playlist Abstract Algebra

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Math 031 041917 Taylor's Theorem and the Lagrange Remainder Theorem (no sound)

Motivation: how do you know of the Taylor series converges back to the original function? Statement of Taylor's Theorem (+ Lagrange Remainder Formula). Example application: showing that the Taylor series for the sine recovers the sine (at x = 1; then for general x). Same application for

From playlist Course 3: Calculus II (Spring 2017)

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Chapter 3: Lagrange's theorem, Subgroups and Cosets | Essence of Group Theory

Lagrange's theorem is another very important theorem in group theory, and is very intuitive once you see it the right way, like what is presented here. This video also discusses the idea of subgroups and cosets, which are crucial in the development of the Lagrange's theorem. Other than c

From playlist Essence of Group Theory

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Group theory 4: Lagrange's theorem

This is lecture 4 of an online course on mathematical group theory. It introduces Lagrange's theorem that the order of a subgroup divides the order of a group, and uses it to show that all groups of prime order are cyclic, and to prove Fermat's theorem and Euler's theorem.

From playlist Group theory

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Calculus BC - Unit 5 Lesson 2: Lagrange Error Bound

Calculus BC - Taylor's Remainder Theorem and the Lagrange Error Bound

From playlist AP Calculus BC

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Mirna Džamonja: Universal א2-Aronszajn trees

Recorded during the meeting "XVI International Luminy Workshop in Set Theory" the September 14, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Au

From playlist Logic and Foundations

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Subderivatives and Lagrange's Approach to Taylor Expansions | Algebraic Calculus Two | Wild Egg

The great Italian /French mathematician J. L. Lagrange had a vision of analysis following on from the algebraic approach of Euler (and even of Newton before them both). However Lagrange's insights have unfortunately been largely lost in the modern treatment of the subject. It is time to re

From playlist Algebraic Calculus Two

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Mathematics & Science in History - C. Fraser, 4/26/2019

On April 26-27 2019, the Division of Humanities & Social Sciences at Caltech hosted a conference in honor of Jed Z. Buchwald, “Looking Back as We Move Forward: The Past, Present, and Future of the History of Science.” This event was sponsored by the Division of the Humanities & Social Sci

From playlist Looking Back as We Move Forward - A Conference in Honor of Jed Z. Buchwald - 4/26-27/2019

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On Mastering the Facts - S. Kingsland - 4/27/2019

On April 26-27 2019, the Division of Humanities & Social Sciences at Caltech hosted a conference in honor of Jed Z. Buchwald, “Looking Back as We Move Forward: The Past, Present, and Future of the History of Science.” This event was sponsored by the Division of the Humanities & Social Sci

From playlist Looking Back as We Move Forward - A Conference in Honor of Jed Z. Buchwald - 4/26-27/2019

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Math 031 Spring 2018 043018 Lagrange Remainder Theorem

Definition of Taylor polynomial; of remainder (error). Statement of Lagrange Remainder Theorem. Example.

From playlist Course 3: Calculus II (Spring 2018)

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Lecture 1: Invitation to topos theory

This talk introduces the motivating question for this semester of the Curry-Howard seminar, which is how to organise mathematical knowledge using topoi. The approach sketched out in the talk is via first-order theories, their associated classifying topoi, and adjoint pairs of functors betw

From playlist Topos theory seminar

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From 'The Girls of Nineteen-Twenty-Six' by James Laver - Read by John Gielgud

An excerpt from We Were Happy There by Allan Bennet. Recorded by MCA Records Ltd. in 1969. Copyright by Phonographic Performance Ltd.

From playlist John Gielgud's Recordings

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Archive Picks - 28 August to 11 September 2017 | British Pathé

Here’s our selection of films that may be of use to news editors and journalists in covering important anniversaries, contextualising current events or illustrating trending topics. To explore these themes, check out the complete films showcased in this video here: Ingrid Bergman Dies:

From playlist Archive Picks | British Pathé

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Number Theory | Lagrange's Theorem of Polynomials

We prove Lagrange's Theorem of Polynomials which is related to the number of solutions to polynomial congruences modulo a prime.

From playlist Number Theory

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Matthew Foreman: Welch games to Laver ideals

Recorded during the meeting "XVI International Luminy Workshop in Set Theory" the September 16, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Au

From playlist Logic and Foundations

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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

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Word problems with trigonometry and triangles ex 2

👉 Learn how to solve word problems with triangles. A word problem is a real-life situation which can be modelled mathematically. Word problems involving angles of elevation and depression, straight object leaning against a vertical object, etc, are usually modeled using right triangles. Be

From playlist Solve Word Problems with Right Triangles

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Lagrange multipliers: 2 constraints

Download the free PDF http://tinyurl.com/EngMathYT This video shows how to apply the method of Lagrange multipliers to a max/min problem. Such ideas are seen in university mathematics.

From playlist Several Variable Calculus / Vector Calculus

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Peter Scholze - Liquid vector spaces

Talk at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ (joint with Dustin Clausen) Based on the condensed formalism, we propose new foundations for real functional analysis, replacing complete locally convex vector spaces with a vari

From playlist Toposes online

Related pages

Order theory | Order embedding | Total order | Countable set | Roland Fraïssé | Well-quasi-ordering | Dushnik–Miller theorem | Second-order arithmetic | Sequence | Scattered order | Reverse mathematics