The absolute difference of two real numbers and is given by , the absolute value of their difference. It describes the distance on the real line between the points corresponding to and . It is a special case of the Lp distance for all and is the standard metric used for both the set of rational numbers and their completion, the set of real numbers . As with any metric, the metric properties hold: * , since absolute value is always non-negative. * if and only if . * (symmetry or commutativity). * (triangle inequality); in the case of the absolute difference, equality holds if and only if or . By contrast, simple subtraction is not non-negative or commutative, but it does obey the second and fourth properties above, since if and only if , and . The absolute difference is used to define other quantities including the relative difference, the L1 norm used in taxicab geometry, and graceful labelings in graph theory. When it is desirable to avoid the absolute value function – for example because it is expensive to compute, or because its derivative is not continuous – it can sometimes be eliminated by the identity if and only if . This follows since and squaring is monotonic on the nonnegative reals. (Wikipedia).

Math 101 091117 Introduction to Analysis 05 Absolute Value

Absolute value: definition. Notion of distance. Properties of the absolute value: proofs. Triangle inequality

From playlist Course 6: Introduction to Analysis (Fall 2017)

Absolute versus relative measurements in geometry | Rational Geometry Math Foundations 134

In science and ordinary life, the distinction between absolute and relative measurements is very useful. It turns out that in mathematics this is also an important distinction. We must be prepared that some aspects of mathematics are more naturally measured relatively, rather than absolute

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What is the definition of absolute value

http://www.freemathvideos.com In this video playlist you will learn how to solve and graph absolute value equations and inequalities. When working with absolute value equations and functions it is important to understand that the absolute value symbol represents the absolute distance from

From playlist Solve Absolute Value Equations

Absolute and Relative Extrema From a Graph Explained Intuitively

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Finding Absolute and Relative Extrema From a Graph Explained Intuively. Understanding the difference between relative maximum's and minimum's and absolute maximum's and minimum's.

From playlist Calculus

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From playlist Solving Absolute Value Equations

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This video explains how to determine the difference of two absolute values. http://mathispower4u.com

From playlist Absolute Value

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Watch the full playlist: https://www.youtube.com/watch?v=kcxK3_sROZA&list=PL14bv5vXK2WWuODhGbpPQA0GamV5ohOVb&index=1 Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative. Take a

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Intermediate Algebra Lecture 9.2 Part 2: Solving Absolute Value Equations

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Intermediate Algebra Lecture 9.2: Solving Absolute Value Equations

https://www.patreon.com/ProfessorLeonard Intermediate Algebra Lecture 9.2: Solving Absolute Value Equations

From playlist Intermediate Algebra (Full Length Videos)

Lecture 18: Weierstrass's Example of a Continuous and Nowhere Differentiable Function

MIT 18.100A Real Analysis, Fall 2020 Instructor: Dr. Casey Rodriguez View the complete course: http://ocw.mit.edu/courses/18-100a-real-analysis-fall-2020/ YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP61O7HkcF7UImpM0cR_L2gSw We can show that differentiability implies

From playlist MIT 18.100A Real Analysis, Fall 2020

EEVblog #1268 - DIY Boeing 747 Cockpit Simulator Full Tour

Full tour around, under, and inside the world's most expensive DIY Boeing 747-400 full motion flight simulator under construction. With Rod Redwin from Simulator Solutions: https://simulatorsolutions.com.au/ Forum: https://www.eevblog.com/forum/blog/eevblog-1268-diy-boeing-747-cockpit-sim

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Proof: Reverse Triangle Inequality Theorem | Real Analysis

The reverse triangle inequality tells us how the absolute value of the difference of two real numbers relates to the absolute value of the difference of their absolute values. In particular, |x-y| is greater than or equal to | |x| - |y| |. We'll prove this result in today's lesson. We'll n

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This video explains how to create a line plot with a specific mean and mean absolute deviation. http://mathispower4u.com

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Support: https://www.patreon.com/ProfessorLeonard Cool Mathy Merch: https://professor-leonard.myshopify.com How to find and define Local/Relative Maximum and Minimum and Absolute Maximum and Minimum.

From playlist Precalculus - College Algebra/Trigonometry

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Learn how to solve absolute value equations with extraneous solutions. Absolute value of a number is the positive value of the number. For instance, the absolute value of 2 is 2 and the absolute value of -2 is also 2. To solve an absolute value problem, we first isolate the absolute value

From playlist Solve Absolute Value Equations

Ex: Determine the Absolute Value of a Difference |a-b|

This video explains how to determine the absolute value of a difference of integers. http://mathispower4u.com

From playlist Absolute Value