Convergent sequences are bounded
Convergent Sequences are Bounded In this video, I show that if a sequence is convergent, then it must be bounded, that is some part of it doesn't go to infinity. This is an important result that is used over and over again in analysis. Enjoy! Other examples of limits can be seen in the
From playlist Sequences
Proof: Convergent Sequence is Bounded | Real Analysis
Any convergent sequence must be bounded. We'll prove this basic result about convergent sequences in today's lesson. We use the definition of the limit of a sequence, a useful equivalence involving absolute value inequalities, and then considering a maximum and minimum will help us find an
From playlist Real Analysis
Introduction to Infinite Series
This video introduces infinite series and the concept of a converging and diverging series. http://mathispower4u.yolasite.com/
From playlist Infinite Sequences and Series
Proof: Convergent Sequences are Cauchy | Real Analysis
We prove that every convergent sequence is a Cauchy sequence. Convergent sequences are Cauchy, isn't that neat? This is the first half of our effort to prove that a sequence converges if and only if it is Cauchy. Next we will have to prove that Cauchy sequences are convergent! Subscribe fo
From playlist Real Analysis
The Sum of Convergent Sequences Converges Proof
The Sum of Convergent Sequences Converges Proof If you enjoyed this video please consider liking, sharing, and subscribing. You can also help support my channel by becoming a member https://www.youtube.com/channel/UCr7lmzIk63PZnBw3bezl-Mg/join Thank you:)
From playlist Advanced Calculus
Proof: Sequence (n+1)/n Converges to 1 | Real Analysis
We will prove the sequence (n+1)/n converges to 1. In other words, we're proving that the limit of (n+1)/n as n approaches infinity is 1. We use the epsilon definition of a convergent sequence and the proof is straightforward, following the typical form of a convergent sequence proof. Re
From playlist Real Analysis
How to Prove a Sequence with Two Components Converges
How to Prove a Sequence with Two Components Converges If you enjoyed this video please consider liking, sharing, and subscribing. You can also help support my channel by becoming a member https://www.youtube.com/channel/UCr7lmzIk63PZnBw3bezl-Mg/join Thank you:)
From playlist Advanced Calculus
Proof: The Limit of a Sequence is Unique | Real Analysis
A convergent sequence converges to exactly one limit. That is, the limit of a sequence is unique. We'll prove this by contradiction in today's real analysis video lesson. We assume our convergent sequence converges to a and b, and that they are distinct, as in the limit is not unique. We t
From playlist Real Analysis
Absolutely and Conditionally Convergent Series
This video explains how to determine if a series on conditionally convergent or absolutely convergent. http://mathispower4u.yolasite.com/
From playlist Infinite Sequences and Series
Sergio Zamora (1/20/23): The lower semi-continuity of \pi_1 and nilpotent structures in persistence
When a sequence of compact geodesic spaces X_i converges to a compact geodesic space X, under minimal assumptions there are surjective morphisms $\pi_1(X_i) \to \pi_1(X)$ for i large enough. In particular, a limit of simply connected spaces is simply connected. This is clearly not true for
From playlist Vietoris-Rips Seminar
Polynomial Progressions in Topological Fields and Their Applications to Pointwise... - Mariusz Mirek
Workshop on Dynamics, Discrete Analysis and Multiplicative Number Theory Topic: Polynomial Progressions in Topological Fields and Their Applications to Pointwise Convergence Problems Speaker: Mariusz Mirek Affiliation: Member, School of Mathematics Date: March 02, 2023 We will discuss mu
From playlist Mathematics
Entropy Equipartition along almost Geodesics in Negatively Curved Groups by Amos Nevo
PROGRAM : ERGODIC THEORY AND DYNAMICAL SYSTEMS (HYBRID) ORGANIZERS : C. S. Aravinda (TIFR-CAM, Bengaluru), Anish Ghosh (TIFR, Mumbai) and Riddhi Shah (JNU, New Delhi) DATE : 05 December 2022 to 16 December 2022 VENUE : Ramanujan Lecture Hall and Online The programme will have an emphasis
From playlist Ergodic Theory and Dynamical Systems 2022
C. Sormani - Intrinsic Flat and Gromov-Hausdorff Convergence 1
We introduce various notions of convergence of Riemannian manifolds and metric spaces. We then survey results and open questions concerning the limits of sequences of Riemannian manifolds with uniform lower bounds on their scalar curvature. We close the course by presenting methods and the
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
C. Sormani - Intrinsic Flat and Gromov-Hausdorff Convergence 1 (version temporaire)
We introduce various notions of convergence of Riemannian manifolds and metric spaces. We then survey results and open questions concerning the limits of sequences of Riemannian manifolds with uniform lower bounds on their scalar curvature. We close the course by presenting methods and the
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
Christina Sormani - Sequences of manifolds with lower bounds on their scalar curvature
If one has a weakly converging sequence of manifolds with a uniform lower bound on their scalar curvature, what properties of scalar curvature persist on the limit space? What additional hypotheses might be added to provide stronger controls on the limit space? What hypotheses are requ
From playlist Not Only Scalar Curvature Seminar
Christina Sormani: A Course on Intrinsic Flat Convergence part 5
The lecture was held within the framework of the Hausdorff Trimester Program: Optimal Transportation and the Workshop: Winter School & Workshop: New developments in Optimal Transport, Geometry and Analysis
From playlist HIM Lectures 2015
C. Sormani - Intrinsic Flat and Gromov-Hausdorff Convergence 4
We introduce various notions of convergence of Riemannian manifolds and metric spaces. We then survey results and open questions concerning the limits of sequences of Riemannian manifolds with uniform lower bounds on their scalar curvature. We close the course by presenting methods and the
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
C. Sormani - Intrinsic Flat and Gromov-Hausdorff Convergence 4 (version temporaire)
We introduce various notions of convergence of Riemannian manifolds and metric spaces. We then survey results and open questions concerning the limits of sequences of Riemannian manifolds with uniform lower bounds on their scalar curvature. We close the course by presenting methods and the
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
This video introduces sequences. http://mathispower4u.yolasite.com/
From playlist Infinite Series