Ordinal numbers | Topological spaces
In mathematics, the first uncountable ordinal, traditionally denoted by or sometimes by , is the smallest ordinal number that, considered as a set, is uncountable. It is the supremum (least upper bound) of all countable ordinals. When considered as a set, the elements of are the countable ordinals (including finite ordinals), of which there are uncountably many. Like any ordinal number (in von Neumann's approach), is a well-ordered set, with set membership serving as the order relation. is a limit ordinal, i.e. there is no ordinal such that . The cardinality of the set is the first uncountable cardinal number, (aleph-one). The ordinal is thus the initial ordinal of . Under the continuum hypothesis, the cardinality of is , the same as that of —the set of real numbers. In most constructions, and are considered equal as sets. To generalize: if is an arbitrary ordinal, we define as the initial ordinal of the cardinal . The existence of can be proven without the axiom of choice. For more, see Hartogs number. (Wikipedia).
Find Values Excluded to Guarantee Existence and Uniqueness of Solution to a IVP - y'=f(t,y)
This video explains how to the values of a differential equation must be excluded to guarantee a unique solution exists. dy/dt=f(t,y) http://mathispower4u.com
From playlist Linear First Order Differential Equations: Interval of Validity (Existence and Uniqueness)
Initial Value Problem Using Method of Undetermined Coefficients
This video provides an example of how to solving an initial value problem involving a linear second order nonhomogeneous differential equation. Site: http://mathispower4u.com
From playlist Linear Second Order Nonhomogeneous Differential Equations: Method of Undetermined Coefficients
Find the Interval That a Linear First Order Differential Equation Has a Unique Solution
This video explains how to determine the interval that a first order differential equation initial value problem would have a unique solution. Library: http://mathispower4u.com Search: http://mathispower4u.wordpress.com
From playlist Introduction to Differential Equations
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
Find Two Solutions to a First Order Initial Value Problem
This video explains how to find two solutions to a first order differential equation initial value problem that does not have a unique solution. Library: http://mathispower4u.com Search: http://mathispower4u.wordpress.com
From playlist Introduction to Differential Equations
A road to the infinities: Some topics in set theory by Sujata Ghosh
PROGRAM : SUMMER SCHOOL FOR WOMEN IN MATHEMATICS AND STATISTICS ORGANIZERS : Siva Athreya and Anita Naolekar DATE : 13 May 2019 to 24 May 2019 VENUE : Ramanujan Lecture Hall, ICTS Bangalore The summer school is intended for women students studying in first year B.A/B.Sc./B.E./B.Tech.
From playlist Summer School for Women in Mathematics and Statistics 2019
A14 Nonhomegeneous linear systems solved by undetermined coefficients
There are two methods for solving nonhomogeneous systems. The first uses undetermined coefficients.
From playlist A Second Course in Differential Equations
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
Ordinals of countable order type beyond infinity
We implement an order of order type beyond the first infinite one, in a straight forward fashion. To that end, we arrange the natural numbers in an order with countably infinitely many jumps. So there are many numbers that come, with respect to our order, after an infinite amount of number
From playlist Programming
Find a General Solution to a Nonhomogeneous DE Using Undetermined Coefficients (Exponential)
This video explains how to determine the general solution to a linear second order differential equation using the method of undetermined coefficients. http://mathispower4u.com
From playlist Linear Second Order Nonhomogeneous Differential Equations: Method of Undetermined Coefficients
Differential Equations | Undetermined Coefficients for a System of DEs
We use the method of undetermined coefficients to solve a nonhomogeneous system of first order linear differential equations. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Systems of Differential Equations
Absolute notions in model theory - M. Dzamonja - Workshop 1 - CEB T1 2018
Mirna Dzamonja (East Anglia) / 30.01.2018 The wonderful theory of stability and ranks developed for many notions in first order model theory implies that many model theoretic constructions are absolute, since they can be expressed in terms of internal properties measurable by the existenc
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields
Another Math of Infinity: Ordinals and "going past infinity"
As a follow up to the last video, here we introduce another math of infinity based on the thought experiment about infinite hotels from last time. Ordinals and well-orders in general give us a another way to think about infinite things; in terms of length and so in the context of ordinals
From playlist The CHALKboard 2022
Differential Equations: First Order Linear Example 1
We present a solution to a first order linear differential equation.
From playlist First Order Linear Differential Equations
Differential Equations: First Order Linear Example 2
We present a solution to a first order linear differential equation.
From playlist First Order Linear Differential Equations
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
This is part of a series of lectures on the Zermelo-Fraenkel axioms for set theory. We discuss the powerset axiom, the strongest of the ZF axioms, and explain why the notion of a powerset is so hard to pin down precisely. For the other lectures in the course see https://www.youtube.com
From playlist Zermelo Fraenkel axioms
WHEN SPACE DOES NOT HAVE DISTANCE: What is the Long Line in Math and Other Examples (Version 2.0)
In many ways metric spaces grant a large amount of structure to a topological space. So it's natural to ask what happens when space does not have distance defined on it. Can we still talk about things like size or even compare these types of spaces to other metrizable spaces? The answer is
From playlist The New CHALKboard
Find a General Solution to a Nonhomogeneous DE Using Undetermined Coefficients (Repeat Term)
This video explains how to determine the general solution to a linear second order differential equation using the method of undetermined coefficients. http://mathispower4u.com
From playlist Linear Second Order Nonhomogeneous Differential Equations: Method of Undetermined Coefficients