# What is Absolute values: Definition and 77 Discussions

In mathematics, the absolute value or modulus of a real number x, denoted |x|, is the non-negative value of x without regard to its sign. Namely, |x| = x if x is positive, and |x| = −x if x is negative (in which case −x is positive), and |0| = 0. 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.

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1. ### B Binary variables (Absolute values)

Hello, According to https://www.fico.com/fico-xpress-optimization/docs/latest/mipform/dhtml/chap2s1.html?scroll=ssecabsval the formula for absolute values are : y = | x1 - x2| for two variables x1, x2 with 0 ≤ xi ≤ U Introduce binary variables d1, d2 to mean d1 : 1 if x1 - x2 is the positive...
2. ### Quadratic inequalities with absolute values

I was given a problem to solve that goes like this ##\frac{3}{|x+3|-1}\geq |x+2|## . I got the correct solution for all possible cases and here they are; for ##|x+3|\geq0## and ##|x+2|\geq## i got ##x\epsilon <-2, -2\sqrt{3} ]## and for ##|x+3|\leq0## , ##|x+2|\leq0## I got ##x\epsilon [-5...
3. ### Solving an inequality involving absolute values

Problem Statement : I copy and paste the problem as it appeared in the text to the right. Attempt (mine) : I copy and paste my attempt using Autodesk Sketchbook##^{\circledR}## below. I hope the writing is legible. My answer : I have three answers and confused as to which of them hold...

28. ### Evaluating the integral of absolute values

Homework Statement ∫(0 to 3pi/2) -7|sinx|dx Homework Equations The Attempt at a Solution I am not sure how to treat it as it has an absolute value i assumed that you could remove the -7 to get -7∫|sinx| dx then integrate sinx into -cosx but since there is absolute...
29. ### Intuitive reason absolute values are used for transformations in statistics?

this isn't really homework, but I was just wondering if someone could offer an intuitive reason as to why when random variables are transformed, we use absolute values of derivative of those functions, as opposed to the functions themselves?
30. ### Integrating absolute values over infinity

Homework Statement Find <x> in terms of X0 if X0 is constant and \Psi(x) = \frac{1}{\sqrt{X_0}}e^{\frac{-|x|}{X_0}} and <x> = \int^{\infty}_{-\infty}{\Psi^* x \Psi}dx where Psi* is the complex conjugate of Psi. Since there is no imaginary component, this is effectively Psi2. so, from...
31. ### Inequality with two absolute values

Homework Statement Find all real values of x that satisfy the following inequality. Homework Equations |x-3| > |x + 1| The Attempt at a Solution Splitting up the inequality into cases I get: 1. |x-3| > x + 1 and 2. |x-3| < -x - 1 1. x-3 > x + 1 or x-3 < -x - 1...
32. ### Why do absolute values appear in the simplification of square roots?

Homework Statement Simplify. a) \sqrt{x^6} b) 8 \sqrt{x^7y^{10}} - 10 \sqrt{x^7y^{10}} For b, it's y^10. I can't make it look right for some reason. Mod note: Fixed the exponent. Homework Equations The Attempt at a Solution I can simplify all of them but I don't know when or where I need to...
33. ### An inequality with absolute values

Homework Statement Solve Ix+3I>2 *I is used for absolute value notation The Attempt at a Solution Considering both a) Ix+3I > 0 then Ix+3I= x+3 b) Ix+3I < 0 then Ix+3I= -(x+3) when solved this would yield to; a) x>-3 and x>-1 b) x<-5 and x<-3 from my general reasoning i...
34. ### Replacement of Squaring in Variance Equation: Benefits?

The variance equation basically sums up all the distances between each data value and the mean of the set. The interesting thing is that each distance and squared for a reason that I believe is to make the distance positive, but why don't the statisticians just take the absolute value of each...
35. ### Proofs: Absolute Values and Inequalities

Homework Statement I am wondering if the general approach to these proofs involving absolute values and inequalities is to do them case-wise? Is that the typical approach (unless pf course you see some 'trick')? For example, I have: Prove that if |x-xo| < ε/2 and Prove that if |y-yo| <...
36. ### System of equations incl. complex and absolute values

Homework Statement I'm currently implementing an algorithm in Matlab, however, I've hit a bump, I'm trying to solve the following system of equations: Known variables = a, b, c, d[complex] Unknown variabls = fs, fd, fv, alpha My problem is what to do with the |alpha| since I can't get...
37. ### Complex inequality with absolute values

Homework Statement Determine the values of z \in \mathbb{C} for which |z+2| > 1 + |z-2| holds. Homework Equations Nothing complicated I can think of. The Attempt at a Solution For real values this holds for anything greater than 1/2. If I could figure out the boundaries of the...
38. ### Absolute values resulting in diff-eqs

Homework Statement Consider a simple first-order linear differential equation, such as y' + \tan x y = 0 With initial condition y(0)=C for some constant C. Find all solutions y which satisfy this differential equation on the entire real line. Homework Equations General method for...
39. ### Inequalities involving division of two absolute values

Homework Statement How to solve x for these inequality? Homework Equations |x-2|/|x+3|> (x+2) / (x+1) The Attempt at a Solution (x - 2)/(x + 3) > (x + 2) / ( x+1) the left side holds the condition that is x >= 2 however, I wonder the next step. should I crossly multiply so...
40. ### Solving integrals with absolute values

Homework Statement solve the integral [abs(x+1)(3+abs(x))]/(x+1) between -3 and 1 Homework Equations The Attempt at a Solution when x<-1 then [abs(x+1)(3+abs(x))]/(x+1) = [-(x+1)(3-x)]/(x+1) = -(3-x) when -1<x<0 then [abs(x+1)(3+abs(x))]/(x+1) = (x+1)(3-x)/(x+1) = 3-x when x>0...
41. ### Integration with absolute values

Homework Statement if f(x)=abs(x-2) and g(x)=abs(x), then solve the integral from -1 to 3 of abs(f(x)-g(x))dx Homework Equations The Attempt at a Solution resolved absolute values: when x<0, abs(x-2)-abs(x) = -x-2+x = 2 when 0<x<1, abs(x-2)-abs(x) = (-x+2)-x = 2-2x when 1<x<2...
42. ### Particular solution of nonhomog. euler equation Messy absolute values in integral

Homework Statement Solve the IVP (x^2)y'' + 4xy' - 40y = x^6 for y(1) = 10, y'(1) = 1Homework Equations not so much "equations" but here I try to use variation of parameters to get the particular solution.The Attempt at a Solution FOR THE HOMOGENEOUS SOLUTION: using the substitution y = x^r...
43. ### Solving equation containing absolute values

Homework Statement I have this equation |2x+7| - |6-3x| = 8. The step I did is to replace the || with () and then solve the equation 2x+7-6+3x = 8 X = 7/5 But how do a go about solving for the second solution? With one absolute value I would |2x + 7| = 8 2x + 7 = +-8 2x = -7...
44. ### Understanding Absolute Values.

Hey Guys! I've frequently come by this forum and have finally joined it in hopes that I could get some more conceptual insight in understanding math. One thing that I have trouble with is absolute values. I understand that: |x|= \sqrt{x^2} .. and how it can be defined given restrictions on...
45. ### Minimizing Sum of Absolute Values

Hello all, I am trying to solve a problem based on some computer programming task I am trying to solve, and I have encountered a situation I am having trouble continuing.. Given a function f(x)=|1-x| + |0.5-2x| ... How can I find it's minimum efficiently? This sum may extend to 4 or 5...
46. ### Proofs with continuity and absolute values

Homework Statement -F is a continuous function on [0,1], so let ||f|| be the maximum value of |f| on [0,1] a. Prove that for any number c we have ||cf|| = |c|\ast||f|| b. Prove that ||f + g|| \leq ||f|| + ||g||. c. Prove that ||h - f|| \leq ||h - g|| + ||g - f|| Homework Equations Based...
47. ### HELP Absolute Values on a Complex Plane

Homework Statement Draw |z| on a complex plane, where z = -3+4i Homework Equations N/A The Attempt at a Solution [PLAIN]http://img530.imageshack.us/img530/1786/aaakr.jpg Can anyone please tell me which answer is correct? Both of them have a moduli of 5. So should the circle...
48. ### Confused about equations with absolute values

My calc book rewrites this equation: |y|=e^c|x| As this: y=\pm e^cx But that doesn't really make any sense to me. I know I should understand why we're allowed to do that, but I don't. Could someone please try to explain it to me? I really appreciate your help, thanks!
49. ### Absolute Values and Inequality understanding

Homework Statement I saw this in my real analysis textbook and I have been trying to understand how this equation \left | x-c \right |< 1 you can get this: \left | x \right |\leq \left | c \right | + 1 Homework Equations I wanted to know what steps made this possible ...
50. ### Proving Non-Continuity at (0,0) for f(x,y) = |xy|

Homework Statement Let f(x, y) = |xy|. I want to prove that f is not continuous at (0,0). The Attempt at a Solution To prove that f is not continuous at (0,0) I think I need to show that \lim_{(x, y) \to (0, 0)}|xy| \neq 0 I'm a little confused about the |absolute value|...