Infinity | Hyperbolic geometry | Projective geometry
In geometry, a point at infinity or ideal point is an idealized limiting point at the "end" of each line. In the case of an affine plane (including the Euclidean plane), there is one ideal point for each pencil of parallel lines of the plane. Adjoining these points produces a projective plane, in which no point can be distinguished, if we "forget" which points were added. This holds for a geometry over any field, and more generally over any division ring. In the real case, a point at infinity completes a line into a topologically closed curve. In higher dimensions, all the points at infinity form a projective subspace of one dimension less than that of the whole projective space to which they belong. A point at infinity can also be added to the complex line (which may be thought of as the complex plane), thereby turning it into a closed surface known as the complex projective line, CP1, also called the Riemann sphere (when complex numbers are mapped to each point). In the case of a hyperbolic space, each line has two distinct ideal points. Here, the set of ideal points takes the form of a quadric. (Wikipedia).
This video provides a description of infinity with several examples. http://mathispower4u.com
From playlist Linear Inequalities in One Variable Solving Linear Inequalities
Definition of infinity In this video, I define the concept of infinity (as used in analysis), and explain what it means for sup(S) to be infinity. In particular, the least upper bound property becomes very elegant to write down. Check out my real numbers playlist: https://www.youtube.co
From playlist Real Numbers
Introduction to Limits at Infinity (Part 1)
This video introduces limits at infinity. https://mathispower4u.com
From playlist Limits at Infinity and Special Limits
Examples: Determining Limits at Infinity Graphically
This video provides examples of determining limits at infinity graphically. Complete Video List at http://www.mathispower4u.com
From playlist Limits at Infinity and Special Limits
The definition of limit at infinity (Ch2 Pr8)
A gentle introduction to the formal "epsilon-M" definition for the limit of a function at infinity. This is Chapter 2 Problem 8 from the UNSW MATH1131/1141 Calculus notes. Presented by Dr Daniel Mansfield.
From playlist Mathematics 1A (Calculus)
Limits At Infinity - Additional Examples
This is a second video on limits at infinity that provides additional examples. http://mathispower4u.wordpress.com/
From playlist Limits
How to visualize infinity in concrete terms.
From playlist Summer of Math Exposition 2 videos
Touching Infinity: It's Not Out of Reach
The conventional way to represent the Real Number system is to think of the numbers as corresponding to points along an infinite straight line. The problem is that in this representation there is no place for "infinity". Infinity is not a real number. This video shows an alternate visua
From playlist Lessons of Interest on Assorted Topics
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
Higher Algebra 10: E_n-Algebras
In this video we introduce E_n-Algebras in arbitrary symmetric monoidal infinity-categories. These interpolate between associated algebras (= E_1) and commutative algebras (= E_infinity). We also establish some categorical properties and investigate the case of the symmetric monoidal infin
From playlist Higher Algebra
Markus Spitzweck: A Grothendieck Witt space for stable infinity categories with duality
The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Topology: "Workshop: Hermitian K-theory and trace methods" In the talk we will construct a Grothendieck-Witt space for any stable infinity category with duality. We will show that if we apply our constru
From playlist HIM Lectures: Junior Trimester Program "Topology"
J.-M. Martell - A minicourse on Harmonic measure and Rectifiability (Part 2)
Solving the Dirichlet boundary value problem for an elliptic operator amounts to study the good properties of the associated elliptic measure. In the context of domains having an Ahlfors regular boundary and satisfying theso-called interior corkscrew and Harnack chain conditions (these ar
From playlist Rencontres du GDR AFHP 2019
Charles Rezk - 3/4 Higher Topos Theory
Course at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Slides: https://aroundtoposes.com/wp-content/uploads/2021/07/RezkNotesToposesOnlinePart3.pdf In this series of lectures I will give an introduction to the concept of "infinity
From playlist Toposes online
Algebra and Geometry in perspective by Suresh Nayak
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
Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations. This course is about calculus 2
From playlist Calculus
Limits and algebra continued -- Calculus I
This lecture is on Calculus I. It follows Part I of the book Calculus Illustrated by Peter Saveliev. The text of the book can be found at http://calculus123.com.
From playlist Calculus I
MATH 331: Compactifying CC - part 1- Riemann Sphere, PP^1, One Point Compactification
We describe three compactifications of the complex numbers: The one point compactification, the Riemann Sphere and the complex projective line. In a subsequent video we explain the following facts: *Why all holomorphic functions on the compactification are constant. *Why endomorphism of PP
From playlist The Riemann Sphere
Math 101 Introduction to Analysis 09 092017 The Extended Real Number System; Sequences
Extended real number system as a set; as an ordered set. Comment: all nonempty subsets have least upper bounds. Is not a field. Conventions. Definition of a sequence. Examples of sequences.
From playlist Course 6: Introduction to Analysis (Fall 2017)
Elliptic curves: point at infinity in the projective plane
This video depicts point addition and doubling on elliptic curve in simple Weierstrass form in the projective plane depicted using stereographic projection where the point at infinity can actually be seen. Explanation is in the accompanying article https://trustica.cz/2018/04/05/elliptic-
From playlist Elliptic Curves - Number Theory and Applications