Special functions | Norms (mathematics) | Real numbers
In mathematics, the absolute value or modulus of a real number , denoted , is the non-negative value of without regard to its sign. Namely, if x is a positive number, and if is negative (in which case negating makes positive), and . For example, the absolute value of 3 is 3, and the absolute value of −3 is also 3. The absolute value of a number may be thought of as its distance from zero. Generalisations of the absolute value for real numbers occur in a wide variety of mathematical settings. For example, an absolute value is also defined for the complex numbers, the quaternions, ordered rings, fields and vector spaces. The absolute value is closely related to the notions of magnitude, distance, and norm in various mathematical and physical contexts. (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)
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From playlist Solving Absolute Value Equations
How To Solve an Absolute Value Equation and Test Our Solutions when They Do Not Work
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
Learn how to evaluate left and right hand limits of a function
👉 Learn how to evaluate the limit of an absolute value function. The limit of a function as the input variable of the function tends to a number/value is the number/value which the function approaches at that time. The absolute value function is a function which only takes the positive val
From playlist Evaluate Limits of Absolute Value
Learn How To Solve an Absolute Value Equation and Check Your Answers
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
Solving Absolute value equations with a variable on both sides
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
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
Proofs from calculus -- Proof Writing 20
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From playlist Proof Writing
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
From playlist Real Analysis
proving limits -- proof writing examples 20
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From playlist Proof Writing
Proof: Limit Law for Quotient of Convergent Sequences | Real Analysis
We prove the limit law for the quotient of convergent sequences. If a_n converges to a and b_n converges to b, then the sequence a_n/b_n converges to a/b, provided that b isn't 0, and each b_n is not 0. Put simply, the quotient of convergent sequences converges to the quotient of their lim
From playlist Real Analysis
Linear Absolute Value Functions & Graphical Attributes
What is the Absolute Value at 1:09 Defining Linear Absolute Value Function at 7:14 Graphing a Linear Absolute Value Function with a T-table at 14:42 Identifying the Graphical Attributes at 22:01 (Intervals of Increasing and Decreasing, Absolute Maximum or Minimum, Domain, Range) Last
From playlist Algebra 1
ʕ•ᴥ•ʔ Solve Absolute Value Functions with Examples
Quickly master how to solve absolute value functions. Watch more lessons like this and try our practice at https://www.studypug.com/algebra-help/absolute-value/absolute-value-functions Absolute value is basically the distance between “number” and “zero” on a number line. We will look int
From playlist GCSE Exam Prep
Triangle Inequality In this video, I define the concept of an absolute value and use it to prove the triangle inequality in R, which is the most important inequality that we'll use in analysis. Enjoy! Check out my Real Numbers Playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmC
From playlist Real Numbers
Definition of a Limit Epsilon Delta Proof 3 Examples Calculus 1
I introduce the precise Definition of a Limit and then work through three Epsilon Delta Proofs Delta Epsilon Limit Proof involving a linear function at 11:31 Epsilon Delta Proof involving a quadratic function at 28:38 Epsilon Delta Proof involving an absolute value function at 47:29 Links
From playlist Calculus
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)
Math 023 Fall 2022 090722 Absolute Values (continued)
Recall: what is the definition of the absolute value? Exercise: what is |-x| if x is negative? What is |x| if x is negative? Properties of the absolute value. Examples. Geometric interpretation of |x-y| as the distance between x and y. Examples: using that interpretation to describe
From playlist Course 1: Precalculus (Fall 2022)
How To Solve an Absolute Value Equation when There is Only One Solution
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