What is Absolute: Definition and 1000 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. M

    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...
  2. L

    Can absolute value functions be considered polynomial functions?

    Are lx3l or lxl3 polynomials? If not, what would be a good example of a cubic polynomial function (R \rightarrow R) that doesn't cover all real numbers in its codomain?
  3. W

    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...
  4. T

    Arctan absolute value problem, calculus 1

    Homework Statement prove |arctan(x)-arctan(y)| \leq |x-y| The Attempt at a Solution I tried separating cases: 1. both x and y are in the same quadrant; 2. x and y are not in the same quadrant; 3. x and y are zero (trivial); 4. either x or y is zero. Now, i can see why each of these is...
  5. H

    How Do You Solve Absolute Value Inequalities with Double Variables?

    how do you go about solving abs value inequalities with double variables when the abs value bars are on both the variables? eg; |x| + or - |y| =, >, <, a
  6. E

    Inequality and absolute value proof

    Homework Statement prove that llal-lbll\leqla-bl Homework Equations Triangle inequality lx+yl\leqlxl+lyl The Attempt at a Solution Let a=(a-b)+b By using the triangle inequality we get lal-lbl\leqla-bl Then from here I am not sure what I can do. I would like to say on the left...
  7. Y

    Absolute motion's point of reference

    According to special relativity acceleration is an absolute motion, so according to what is it moving?
  8. T

    Area between curves, with an absolute value function

    Homework Statement Then find the area S of the region. (between the curves) Homework Equations A = \int_a^b f(x)-g(x) dxThe Attempt at a Solution First I plotted both equations, determined the top and the bottom functions and found where they intersected (calculator). Then I set up the...
  9. 3

    Absolute and Relatiave Uncertainty (partial derivatives)

    Homework Statement Calculate the following, expressing all results with uncertainties both in absolute and relative (percentage) form: a) A + B b) A x B c) Asin(theta) d) A^2 / Bcos(theta) The relevant formula for the absolute uncertainty is below, but i have no idea how to...
  10. N

    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!
  11. Ivan Seeking

    News Are women people? The inconsistency of absolute originalism

    As Stephen Colbert pointed out http://news.yahoo.com/s/time/08599202066700 Amendment XIV http://en.wikipedia.org/wiki/Fourteenth_Amendment_to_the_United_States_Constitution Emphasis mine. Yet Scalia voted for corporate personhood. Frankly, I don't know what to say. How did this...
  12. T

    Exploring the Effects of Absolute Zero on Time

    If time requires movement in space time in order for change and hence time to occur then how does absolute zero in temperature effect time since no molecular or atomic movement is possible at such temperature? Does vibration constitute movement that can affect time in relativistic terms? Is it...
  13. L

    Absolute Value Inequality: How to Solve and Graph

    Homework Statement l [3/(x-1)] - 5l < 4Homework Equations The Attempt at a Solution My 1st step was to make the inequality like this. -4 < 3/(x-1) - 5 < 4 and then i multiplied (x-1) to both left and right side and as well as to the 5. but in the end, my result turns out to be...
  14. W

    Integral of exponential absolute functions

    Hello, I am having difficulty solving the following integral: \int^{\infty}_{-\infty}e{-(a|x|+ikx)}dx I have tried to use an explicit form of the absolute, eg. -(a|x|+ikx) = \left\{\stackrel{-(ik+a)x\ x>0} {-(ik-a)\ x<0} Does this allow me to separate the integral into a sum of two...
  15. C

    Y= l sin x l < absolute value of sinx

    Homework Statement y= l sin x l < absolute value of sinx Homework Equations The Attempt at a Solution y= l sin x l= sinx, if x>0 -sinx, if x< 0 0, if x=0 I get that part, but when i draw the graph I don't get it
  16. P

    How to Solve Rational Inequalities?

    Homework Statement Solve (x+2)/(x+1) -2 < 0 Homework Equations LCD: x + 1 The Attempt at a Solution (x+2-2x-2)/(x+1) < 0 (-x )/(x+1) < 0 But somehow, I got the wrong answer. The answer is (4, 7]. But I don't know where I went wrong.
  17. P

    Differentiating absolute quadratic

    Homework Statement For the function y= |x2-4x+3| a. Sketch the function b. Is the function continuous? Explain. c. Is the function differentiable everywhere? explain d. find gradient of curve at the point where x = 3/2 Homework Equations chain rule, differentiating... The...
  18. D

    Proofs using absolute value with Triangle/AGM Inequality

    Homework Statement *Sorry I could not get the math symbols to work properly so I did it by hand. I hope this isn't too much trouble. Prove: | sqrt( x ) - sqrt( y ) | <= | sqrt ( x - y ) | for x, y >= 0 Hint: Treat the cases x >= y and x <= y separately. I am new to proofs and we can't use...
  19. A

    Why does Newtonian mechanics include relative motion between inertial frames?

    I know that in Newtonian mechanics an inertial frame of reference moves relative to absolute space. But why does Newtonian mechanics include the contention that two inertial reference frames move relative to each other? It seems that if you have an absolute reference frame then there is no...
  20. K

    Double integrals with absolute function

    Homework Statement [PLAIN]http://img704.imageshack.us/img704/453/50838240.jpg i have trouble with absolute function, can somebody help me how to start
  21. V

    Absolute Value of e(i): Why is it Equal to 1?

    Why does |e^i| = 1 ?
  22. A

    What values satisfy this equation: ((2x-7)/(x3+3))<(9/x)<=x²-5x+9?

    Excuse me for my english; Decide for all the x so this works out; ((2x-7)/(x3+3))<(9/x)<=x²-5x+9 where "<=" is the same as "and =". Having some troubles getting the right values between (9/x)<=x²-5x+9, but otherwise it's fine.. hope you can help me!
  23. Z

    Absolute value on both side of equation

    I solved this absolute value equation and I am confuse about the answer given in the book for this question, the answer in the book is x > = 0 or x = -2/3 please tell me how can I get this answer from the following solution. Please tell the method which should be true for all such type of...
  24. Z

    Solving Absolute Value Problem: x ≤ 3

    Suppose we have this absolute value question | x-3 | = 3 – x If we solve this question we break it as X - 3 = 3 – x or -(x - 3) = 3 - x Now if we solve it we come to know that the part on right is true for all real numbers And the part on the left is true for only 3 I also have read that...
  25. C

    Minimize expected value of the absolute difference

    Homework Statement Let X be a continuous random variable with median m. Minimize E[|X - b|] as a function of b. Hint: Show that E[|X - b|] = E[|X - m|] + 2 \int (x - b) f(x) dx , where the integral is from b to m. Homework Equations The Attempt at a Solution I wanted to try a...
  26. B

    Is it possible to determine absolute speed?

    I started posting to what seemed to be a related thread here: https://www.physicsforums.com/showthread.php?p=2825641&posted=1#post2825641 After concluding I was hijacking another thread, I am posting here. The concept is I think that, in theory, one can determine absolute speed. Am I the one...
  27. S

    Absolute Value Inequalities: Solving and Graphing

    Homework Statement Solve the inequality and sketch the graph of the solution on the real number line. Homework Equations |x - a|< or equal to b, b > 0 Let us imagine that the ">" and "<" signs also include "equal to" except for the condition, b > 0, in order to solve this...
  28. N

    Absolute vs. Relative Maxima and Minima

    Homework Statement I do not have a specific homework problem, but could someone please clarify this for me? QUESTION: When you have an absolute maxima (or minima), how can you tell if it is ALSO a relative maxima (or minima)? I understand how to find absolute extrema on a closed...
  29. E

    Is time absolute or dynamical in LQG and string theory?

    regarding the problem of time in QG, Is time absolute or dynamical in LQG? string theory? How does LQG and string theory deal with time in singularities in the center of black holes?
  30. C

    Relativity says that there is no absolute simultaneity. Quantum

    Relativity says that there is no absolute simultaneity. Quantum mechanics with its entanglement seems to imply absolute simultaneity. And in between these two I am the one who gets confused. :smile: :confused: Please Help.
  31. K

    Expectation of an absolute value

    Homework Statement I have E(a) = 0, E(b) = x but E(|a+b|)=?? where E is the expectations operator and x is a known constant which is greater than zero. Homework Equations Any one know how I would go about determining E(|a+b|)?
  32. R

    Light at Absolute Zero: Answers to Your Questions

    Hi, I'd like to know how does electromagnetic radiation behave at absolute zero temparature ? pls let me know. Thanks in advance !
  33. J

    How Can You Determine the Right Ascension of a Star with a Meridian Circle?

    Hi, With a meridian circle, you can determine the latitude of your location (Horrebow-Talcott method) but also deriving time if you know the right ascension of a star. However, I'd like to know how to determine right ascension of a star with a meridian circle. If you know the right...
  34. B

    Calculating distance using absolute and apparent visual magnitudes

    Is there an equation for calculating the distance of a star if you have the values for apparent visual magnitude and absolute visual magnitude?
  35. C

    Can Absolute Velocity be Measured with Cosmic Background Radiation?

    Greetings, I have heard that one can not know one's absolute velocity, only one's velocity relative to other objects. But wouldn't the cosmic background radiation be blueshifted in the direction of motion and redshifted in the oposite direction? Thanks
  36. I

    Infinity symbol inside of an absolute value Tattoo

    I've been thinking about getting a tattoo. I was considering getting the infinity symbol inside of an absolute value. Or the absolute value of infinity. Whichever you prefer. How mathematically correct is that? The absolute value of infinity simplified is infinity is it not? Will I completely...
  37. P

    What happens when light is brought to an absolute stop?

    http://www.sciencedaily.com/releases/2010/06/100627072458.htm According to the above article, light was brought to a complete stop during an experiment. What confuses me is that, if light has no mass, and is then manipulated to have no velocity either (which means there is no frequency and...
  38. J

    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 ...
  39. Topher925

    Understanding Angular Momentum in Space | SR/GR and Centrifugal Force Explained

    I'm having trouble understanding angular momentum and how it relates to SR/GR. To keep it simple, if I'm in space and all matter and energy is removed (ie. reference frames) and I start rotating at a specific velocity will I feel my arms and legs being pulled out? If the only possible frame of...
  40. Y

    Exploring the Possibility of Absolute Rest

    Sorry if this question seems more philosophical than scientific. It's my first post in this forum. I love learning about the way the universe works and I always have lots of questions :-) Alright, so to my point. It seems like the theory of relativity says that the faster you move (plus how...
  41. T

    Absolute Magnitude of Lightbulb

    Homework Statement By comparing with the luminosity of the Sun, calculate the absolute magnitude of a 60W lightbulb. [THe absolute magnitude of the Sun is +4.75; you may ignore colour differences] Homework Equations m-M=5log(d/10pc) f = \frac{L}{4\pi d^{2}} m1 - m2 = -2.5long(f1 / f2) The...
  42. K

    Absolute Value Proof: Showing |a|=sqrt(a^2) and |a/b|=|a|/|b|

    Homework Statement If a,b are real numbers and b does not equal zero show that |a|=sqrt(a^2) and |a/b|=|a|/|b|. Homework Equations I know that |ab|=|a||b| and a^2 = |a|^2 The Attempt at a Solution Attempt at showing that |a|=sqrt(a^2): |a|=sqrt(a^2) |a|^2=(sqrt(a^2))^2...
  43. B

    Is Using Absolute Value for Infinity Common Practice in Limits?

    Hi, I came across a book which looks at a problem like \lim_{x \to 0}\frac{1}{x} So you approach from 0-, and get -∞, approach from 0+, get ∞ Then it would write the answer as \lim_{x \to 0}\frac{1}{x} = \left| \infty \right| It looks bizarre to me. How do you parse this? Is...
  44. D

    Minimize parameter for Least Absolute Deviation LAD

    How to compute \beta = arg min_\beta \sum_{i=1}^N {|y_i - x_i^T \beta|
  45. Z

    Exploring the Invariance of Light Speed in Special Relativity"

    Consider this thought experiment. Second postulate of SR (invariance of c) says that the speed of light is measured the same for all inertial observers regardless of their relative KE. To better understand what that means I try to imagine how would that look from a perspective of the moving...
  46. majormuss

    Absolute Value Question: Solving |2x - 1| = x^2 with Step-by-Step Guide

    Homework Statement how do I solve this? I am confused... |2x - 1| = x^2 Homework Equations The Attempt at a Solution when i tried it I ended up with a solution set of (1,-1). But the official answer is quite different so I am confused!
  47. Faradave

    Absolute light speed or velocity or both?

    "Absolute" light speed or velocity or both? Consider an inverse of Einstein's light clock. On a cartesian plane in a vacuum, a beam of light emanates from the origin at 45 degrees with velocity c. Is it OK that the x and y component velocities are each less than c (i.e. c divided by sqrt 2)...
  48. L

    A basic function question - with a strange absolute value placement

    Homework Statement If f(x) is equal to... x+9 if x<-3 -2x if |x|\leq 3 -6 if x > 32. The attempt at a solution The first and third "segments" of when the function is defined as being x+9 and -6 are pretty straightforward to me, however I am unaware of the significance of the placement of the...
  49. I

    Uniform Distribution, Absolute Value

    Homework Statement Find the CDF of |X|, given that X is a random variable, uniformly distributed over (-1,3). Is |X| uniformly distributed? If yes, over what interval?Homework Equations The Attempt at a Solution I found so far that: Setting Y=|X| Then: Y \in (1,3) F_{Y}(y)=P\left\{Y\leq...
  50. S

    Integrating an absolute function

    Homework Statement 1 ⌠ | 10^(1/2)*(x^5)+(5*x^(1/5)) | dx ⌡ −1 Homework Equations once the absolute value is gone you can just integrate the function The Attempt at a Solution how do you get rid of the absolute, and how do you then integrate it, do you use the product rule...
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