Abstract algebra

Absolute value (algebra)

In algebra, an absolute value (also called a valuation, magnitude, or norm, although "norm" usually refers to a specific kind of absolute value on a field) is a function which measures the "size" of elements in a field or integral domain. More precisely, if D is an integral domain, then an absolute value is any mapping |x| from D to the real numbers R satisfying: It follows from these axioms that |1| = 1 and |-1| = 1. Furthermore, for every positive integer n, |n| = |1 + 1 + ... + 1 (n times)| = |−1 − 1 − ... − 1 (n times)| ≤ n. The classical "absolute value" is one in which, for example, |2|=2, but many other functions fulfill the requirements stated above, for instance the square root of the classical absolute value (but not the square thereof). An absolute value induces a metric (and thus a topology) by (Wikipedia).

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Absolute Value Equations

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From playlist Solving Absolute Value Equations

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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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Absolute Value Algebra 2

In this problem, we solve an absolute value problem with a variable.

From playlist Algebra 2 Chapter 1 Take Home Test

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INTALG 4 3: Absolute Value Equalities

We describe absolute value for the real numbers and give a procedure for solving equations containing absolute value terms. Many examples are given.

From playlist COLLEGE ALGEBRA (SPRING 2020)

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Absolute Value Equations

Watch more videos on http://www.brightstorm.com/math/algebra

From playlist Algebra I

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Algebra Absolute Value Inequalities

Algebra Absolute Value Inequalities

From playlist Algebra

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Solve |x + 7|=10 (Step by Step Solution)

How to solve an absolute value equation. For more in-depth math help check out my catalog of courses. Every course includes over 275 videos of easy to follow and understand math instruction, with fully explained practice problems and printable worksheets, review notes and quizzes. All co

From playlist GED Prep Videos

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Understand how to solve an absolute value equation

How to solve an absolute value equation and a review of the definition of absolute value. For more in-depth math help check out my catalog of courses. Every course includes over 275 videos of easy to follow and understand math instruction, with fully explained practice problems and printa

From playlist GED Prep Videos

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|– 8| = ? What is the absolute value?

How to find the absolute value of a number. For more in-depth math help check out my catalog of courses. Every course includes over 275 videos of easy to follow and understand math instruction, with fully explained practice problems and printable worksheets, review notes and quizzes. Al

From playlist GED Prep Videos

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| - 5 | = What’s Really ABSOLUTE VALUE?

TabletClass Math: https://tcmathacademy.com/ Math help with absolute value. For more math help to include math lessons, practice problems and math tutorials check out my full math help program at https://tcmathacademy.com/ Math Notes: Pre-Algebra Notes: https://tabletclass-math.c

From playlist GED Prep Videos

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How do you solve this Type of Equation? Let’s learn the steps…

Learn how to solve an absolute value equation. For more in-depth math help check out my catalog of courses. Every course includes over 275 videos of easy to follow and understand math instruction, with fully explained practice problems and printable worksheets, review notes and quizzes. A

From playlist GED Prep Videos

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Pre-Algebra: Absolute Value

Learn Absolute Value - a critical skill for Pre-Algebra students. For more in-depth math help check out my catalog of courses. Every course includes over 275 videos of easy to follow and understand math instruction, with fully explained practice problems and printable worksheets, review

From playlist GED Prep Videos

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8|2x + 3|=16, let’s solve this type of algebra equation

How to solve an absolute value equation - practice problem. For more in-depth math help check out my catalog of courses. Every course includes over 275 videos of easy to follow and understand math instruction, with fully explained practice problems and printable worksheets, review notes

From playlist GED Prep Videos

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Absolute Value Inequalities – How to Solve

TabletClass Math: https://tcmathacademy.com/ How to solve absolute value inequalities. For more math help to include math lessons, practice problems and math tutorials check out my full math help program at https://tcmathacademy.com/ Math Notes: Pre-Algebra Notes: https://ta

From playlist GED Prep Videos

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y=|x - 5| + 7 Absolute Value Equation Let’s Graph Step-by-Step….

TabletClass Math: https://tcmathacademy.com/ Algebra help with graphing an absolute value equation to include finding the vertex. For more math help to include math lessons, practice problems and math tutorials check out my full math help program at https://tcmathacademy.com/ Math

From playlist GED Prep Videos

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Brainstorming: The Meaning of Absolute Value

In this video, we learn the definition of absolute value and see a few examples. College Algebra homepage: http://webspace.ship.edu/jehamb/calg.html

From playlist College Algebra

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Solve the Absolute Value Equation – 3 Steps

TabletClass Math: https://tcmathacademy.com/ How to solve absolute value equations. For more math help to include math lessons, practice problems and math tutorials check out my full math help program at https://tcmathacademy.com/ Math Notes: Pre-Algebra Notes: https://table

From playlist GED Prep Videos

Related pages

Field of fractions | Prime ideal | Norm (mathematics) | Quotient ring | Topological space | Integral domain | Rational function | Absolute value | Positive-definite function | Finite field | Subring | Valuation ring | Zero divisor | Maximal ideal | Ostrowski's theorem | Cauchy sequence | Archimedes | Algebra | Valuation (algebra) | Alexander Ostrowski | Field extension | Irreducible element | Equivalence class | Function (mathematics) | Field (mathematics) | Integer | Embedding | Algebraic number theory | Ring (mathematics) | P-adic valuation | Local ring | Nicolas Bourbaki | Square root | P-adic number | Complete metric space | Triangle inequality