Order theory | Topology | Sets of real numbers
In mathematics, a (real) interval is a set of real numbers that contains all real numbers lying between any two numbers of the set. For example, the set of numbers x satisfying 0 ≤ x ≤ 1 is an interval which contains 0, 1, and all numbers in between. Other examples of intervals are the set of numbers such that 0 < x < 1, the set of all real numbers , the set of nonnegative real numbers, the set of positive real numbers, the empty set, and any singleton (set of one element). Real intervals play an important role in the theory of integration, because they are the simplest sets whose "length" (or "measure" or "size") is easy to define. The concept of measure can then be extended to more complicated sets of real numbers, leading to the Borel measure and eventually to the Lebesgue measure. Intervals are central to interval arithmetic, a general numerical computing technique that automatically provides guaranteed enclosures for arbitrary formulas, even in the presence of uncertainties, mathematical approximations, and arithmetic roundoff. Intervals are likewise defined on an arbitrary totally ordered set, such as integers or rational numbers. The notation of integer intervals is considered . (Wikipedia).
Measurement, approximation and interval arithmetic (I) | Real numbers and limits Math Foundations 81
This video introduces interval arithmetic, first in the context of natural numbers, and then for integers. We start with some remarks from the previous video on the difficulties with irrational numbers, sqrt(2), pi and e. Then we give some general results about order (less than, greater
From playlist Math Foundations
Measurement, approximation + interval arithmetic (II) | Real numbers and limits Math Foundations 82
We continue on with a short intro to interval arithmetic, noting the difference between the laws of arithmetic over the natural numbers and the integers. The case of rational number intervals is also briefly discussed. We end the lecture with some remarks on the vagueness of ``real number'
From playlist Math Foundations
Closed Intervals, Open Intervals, Half Open, Half Closed
00:00 Intro to intervals 00:09 What is a closed interval? 02:03 What is an open interval? 02:49 Half closed / Half open interval 05:58 Writing in interval notation
From playlist Calculus
Interval Notation (What is It?)
Interval Notation Versus Inequality Notation. Learn the difference in this video by Mario's Math Tutoring. We discuss the difference between a closed interval and an open interval. Also we discuss how infinity works with interval notation. Interval Notation is often used when writing the
From playlist Algebra 2
Interval Notation (1 of 2: Bounded intervals)
More resources available at www.misterwootube.com
From playlist Working with Functions
College Algebra Brainstorming: Interval and Inequality Notation
In this video, we explore the interval and inequality notation that is used to describe sets of numbers.
From playlist College Algebra
Intervals: Given the Graph of an Interval, State as an Inequality and Using Interval Notation
This video provides several examples of how to express an interval given as graph using an inequality and using interval notation. Site: http://mathispower4u.com
From playlist Using Interval Notation
Modes of Minor and other Scales | Maths and Music | N J Wildberger
We use the mathematical 12 tone chromatic scale as a framework for an expanded view of modes in music, focusing first on minor scales, and then branching out to other scales. This frees us from the somewhat limiting pre-occupation with the usual Dorian, Lydian, Mixolydian etc modes for the
From playlist Maths and Music
Rethinking musical note naming from a mathematical point of view | Maths and Music | N J Wildberger
Let's step back a bit from our piano focused notation for naming musical notes, and adopt a more mathematical, logical terminology. This will have major advantages to our understanding of the structure of intervals, scales, modes and chords going forward. We use this notation to discuss th
From playlist Maths and Music
Math 101 Introduction to Analysis 110415: Continuity (two versions)
Continuity: definition of (actually sequential continuity); examples; standard definition involving neighborhoods; examples.
From playlist Course 6: Introduction to Analysis
The Mathematical Problem with Music, and How to Solve It
There is a serious mathematical problem with the tuning of musical instruments. A problem that even Galileo, Newton, and Euler tried to solve. This video is about this problem and about some of the ways to tackle it. It starts from the basic physics of sound, proves mathematically why s
From playlist Summer of Math Exposition 2 videos
Math for Game Developers: Fundamentals of Calculus
This video is a gentle introduction to the fundamentals of Calculus for Physics and Game Programmers. We'll start by looking at the basic concepts of physics simulation, deltatime, and proceed to discuss continuous functions and discrete functions. You'll learn about differentiation and
From playlist Summer of Math Exposition Youtube Videos
Hiraoka Yasuaki (8/30/21): On characterizing rare events in persistent homology
Indecomposables obtained through decompositions of persistent homology are regarded as topological summary of real data. However, as is well known, there exist pathologically complicated indecomposables in multi-parameter persistent homology in purely algebraic setting, and this fact makes
From playlist Beyond TDA - Persistent functions and its applications in data sciences, 2021
Lecture with Ole Christensen. Kapitler: 00:00 - Boundedness/Supremum; 05:00 - Example; 08:00 - Maximum Value; 09:00 - Example: Sup Vs. Max; 12:45 - Theorem: Maximum Is Attained On Closed And Bounded Intervals; 15:30 - Vectorspace Of Continuous Functions; 22:00 - Norm On C[A,B]; 36:45 - Exa
From playlist DTU: Mathematics 4 Real Analysis | CosmoLearning.org Math
An Intuitive Introduction to Motivic Homotopy Theory - Vladimir Voevodsky [2002]
2002 Annual Meeting Clay Math Institute Vladimir Voevodsky, American Academy of Arts and Sciences, October 2002
From playlist Mathematics
TabletClass Math http://www.tabletclass.com . This explains interval notation and set builder notation. Set notation is used in more advance math like Pre-Calculus and higher.
From playlist Pre-Calculus / Trigonometry
Robert Tichy: Quasi-Monte Carlo methods and applications: introduction
VIRTUAL LECTURE Recording during the meeting "Quasi-Monte Carlo Methods and Applications " the October 28, 2020 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematician
From playlist Virtual Conference