Absolute Definition and 1000 Threads

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. G

    A natural log inequality with absolute value

    Homework Statement F(x) = (8-12ln|x|)/(x^4) > 0 (a) For what values of x is the expression F(x) defined? Write your answer in interval notation. (b) At what value(s) of x is the expression F(x) equal to zero? If there is more than one answer separate them by commas. (c) The set of...
  2. H

    Calc 1 - derivative of absolute value

    Homework Statement Question is: how can you tell if there are any places you can't take the derivative of an equation that has an absolute value (using logic, not just graphing it) example equations 1. \left|x-5\right| 2. \left| x3+4x2+9x+17 \right| x2+1 3...
  3. N

    Why is the absolute value of x equal to -x for values under zero?

    Here, it says that for the limit f(x) = |x| / x, |x| = { x, x > 0 -x, x < 0 } What I don't undestand is why is |x| = -x for values under zero? Isn't the absolute value for negative values just x and not -x? thanks. EDIT: I don't want to start a new thread, but I got stuck on this...
  4. K

    Finding limits when there is an absolute value in the numerator

    Ok the problem is: lim x->-1 |x+1| / x2-1 (sorry i don't really know how to type the equation out) I think that you have to find the limit as x->-1 from both the left and right sides from right: so I got lim x->-1 = (x+1)/x2-1 = (x+1)/(x+1)(x-1) = 1/(x-1) =1/-1-1 =-1/2 How would I...
  5. J

    Absolute value theorem that I can't convince myself of

    While reading my text, I came across an inequality that I couldn't convince myself of... For real numbers a,b: \left|a+b|<= |a|+|b|. Is this something proven? Or is it an axiom or something?
  6. A

    How do you graph g(x) in terms of f(x) for absolute function?

    The graph of g is interm of f. So how to plot g(x)= f(|x|) and of g(x)=|f(x)|. Is it jus a 'V' shape one.This problem is in Spivak Textbook, Chapter 4. Thanks to all.:confused:
  7. S

    Predicting absolute configuration of molecules

    I have a question about something that has been bothering me for a while... In all of my chemistry classes, my professors have always told me that it is impossible to predict which way a chiral molecule will rotate plane-polarized light (i.e., you will see if a molecule is D or L, but, saying...
  8. T

    How Do You Solve Absolute Value and Quadratic Functions Together?

    Homework Statement a. Find the value of x such as fx < gx where fx = |2x -1| and gx = x(2-x) b. evaluate \displaystyle\int^1_0 [gx - fx]\,dx Homework Equations none The Attempt at a Solution For question a I make it into 2 equation to 2x-1 = 2x-x^2 and 1 - 2x = 2x - x^2. I solve it and find...
  9. S

    Rigorous proof of basic absolute value theorem?

    Rigorous proof of basic "absolute value" theorem? Hey :) I'm working through a Real Analysis text, and I came across this theorem and "proof": http://img352.imageshack.us/img352/6725/proofbx2.png It kind of took me by surprise, because the author of the text is usually very careful about...
  10. V

    Absolute Convergence Tests for Series with Arctan and Alternating Signs

    Homework Statement so this one says the sum of the series starting at n = 1 to inf. of ((-1)^n)arctan(n)/(n^2) Homework Equations Either a ratio test or just an abs. conv. test The Attempt at a Solution not sure how to play this one out, honestly. I see some semblance of hope...
  11. R

    Properties of the Absolute Value

    Just wanted to say hi before I start my post! :smile: As you may know there is a property of the absolute value that states; for a, b \in R; |ab| = |a||b| Well, my friend asked me if I knew a proof for this... but I don't know... How can we prove this statement/property? I know there...
  12. F

    Find Absolute Max/Min of f in Triangular Region

    Homework Statement Find the absolute max and min values of f on the set D. f(x,y)=4xy^3 - (x^2)(y^2) - xy^3 D is the closed triangular region in the xy-plane with vertices (0,0) (0,6) and (6,0). The Attempt at a Solution I found my two critical points to be (1,2) and (2,0). Then I...
  13. S

    Finding Absolute Permeability from Magnetization

    Homework Statement I am doing a project for which I am learning some aspects of electromagnetism by myself, so you can imagine how lost I am. Well, not completely: I was searching for a ferrite with high permeability as a core material. I learned how the octahedral and tetrahedral sites and the...
  14. P

    Finding Absolute Value of Complex Fractions

    Ok this is something i learned few years ago and I am a bit rusty. So i have to find the absolute value of: \frac{1 - 2i}{3 + 4i} + \frac{i - 4}{6i - 8} So first i add the two fractions and i get: \frac{(1 - 2i)(6i - 8) + (i - 4)(3 + 4i)}{(3 + 4i)(6i - 8)} Next i simplify and then...
  15. C

    Absolute Zero and time travel?

    I've been told that as a person approaches the speed of light, time relative to others being viewed slows. when you make the speed of light ( if possible, I’m aware of distance change and mass increase and of the immense amount of energy needed to possibly reach this speed to push that mass)...
  16. G

    Is There an Absolute Time When Events Occur?

    Hi folks - I'm struggling here! Please help ;-) Surely the concept of relativity of simultaneity is an illusion based on the finite speed of light? If an observer witnesses an event (Event A) and is at distance of zero (d=0) from Event A, then that is the TRUE time the event occurred. It is...
  17. L

    Derivative of an absolute value

    I don't get why: \frac{d}{dx}[|u|]=\frac{u}{|u|}(u') Can someone give me an example to which this applies? Can you use any function in place of "u"?
  18. B

    Absolute simultaneity with Einstein synchronized clocks?

    1. Absolute simultaneity with standard synchronized clocks In an one space dimensions approach we propose the following scenario. At the origin O of the inertial reference frame I we find a clock C0(0) and a source of light S(0). An observer R’ moves with constant speed V in the positive...
  19. M

    Temperature: Absolute infinity

    I heard somewhere that it is a matter of debate whether or not there is an absolutely highest temperature, analogous to absolute zero. This puzzled me because I thought that this is a direct consequence of Einstein's relativity: Temperature is average kinetic energy of a substance. But since...
  20. S

    Absolute speed of light conundrum

    I would greatly appreiciate some insight into this question to allow me to beter understand the nature of relative simultainety. A rocketship is traveling at v=.5c and passes a tree at the instant a lightning bolt strikes it. Now some time later (in referance to the rocket) say the light...
  21. T

    The speed of light as an absolute max

    I realize that this has been experimentally confirmed in any number of ways, based on the external application of energy to a particle. I have read articles on this subject, ranging from the magazine variety to texts by famous physicists, over the last 40 years. My question relates to the...
  22. C

    Is Lorentz transformation absolute

    An observer at the mid point between two frames A and B that are moving toward her, measures each of their speeds to be 0.75c. According to SR, the Lorentz transformation will determine the speed of A and B measured by the other to be less than 1.5c. (in fact less than c) Being aware of the...
  23. R

    Quicky on derivative of absolute value in exponential

    Hey folks, I'm looking for a little guidance in solving the derivative y'(x)of the following function containing an absolute in the exponent: y(x)=e^{a|x|} I'm pretty sure its not as simple as y'(x)=a e^{a|x|} Any suggestions??
  24. D

    Absolute Convergence of Homework Series: Real Parameter p

    Homework Statement \sum_{n=2}^{\infty} \ln \left(1+\frac{(-1)^n}{n^p}\right) p is a real parameter, determine when the series converges absolutely/non-absolutely The Attempt at a Solution I tried to do the limit \lim_{n\rightarrow \infty} \frac{\ln...
  25. S

    Does the Cosmic Background Radiation Provide an Absolute Frame of Reference?

    According to Einstein, there is no absolute frame of reference; no such thing as 'absolute rest'. But does not the Cosmic Background Radiation provide an absolute frame of reference? An object for which this radiation is totally isotropic is at absolute rest; I gather we move relative to it at...
  26. K

    Absolute max/min on an unbounded set

    1) Find the global max and min values of the function f(x,y)=x/[x2+(y-1)2+4] on the first quadrant S={(x,y)|x,y>0} Solution: (from textbook example) f(x,y)>0 on S and f(0,y)=0, so the minimum is zero. Moreover, f(x,y) is less than the smaller of 1/x and 1/(y-1)2, so f vanishes as...
  27. maverick280857

    Minimum Value of Absolute Deviation

    Hi, How can I rigorously prove that the quantity S = \sum_{i=1}^{n}|X_{i} - a| (where X_{1},\ldots,X_{n} is a random sample and a is some real number) is minimum when a is the median of the X_{i}'s? Thanks.
  28. O

    Limit of Absolute Sequence: Is the Sandwich Theorem Applicable?

    Homework Statement Consider the sequence a_n = abs(sin(x))^(1/x) Find the lim a_n if it existsHomework Equations None. This is for my calc 2 class. The Attempt at a Solution We are studying the sandwich theorem, so I thought 0 < M^(1/x) < abs(sin(x))^(1/x) < 1^(1/x). (Because I assumed that...
  29. G

    Can Gas Become Solid at Absolute Zero in a Bottle?

    Homework Statement ive been thinking about this for some time but can't find an answer... gas enters a bottle at a very low pressure, and high temperature, to maximise space between particles. the bottle is then sealed off and the temperture drops to absolute zero, does the gas become solid...
  30. V

    The Absolute Worst Nuclear Reactor Disaster

    This may not be an appropriate place to ask this, and if that is the case please chastise me and cast me out. Given that the members of this forum seem to be very educated and intelligent, especially in regards to these fields I wanted to ask a question. What would be the absolute worst case...
  31. R

    How to measure absolute velocity

    you are in a plane flying east with a head wind of 10 kph. The speed of the plane is measured by measuring the wind speed outside the plane and then adjusting for any head wind. Let's say you get a result (after allowing for the head wind) of of 200 kph. Unbeknownst to you the arm of our...
  32. S

    Verifying the mean value theorum for absolute value function

    Homework Statement a) Find the average value of the function f(x)=|x-1| over [0,2]. b)Verify the mean value theorum for integrals for the function and interval in part (a). Homework Equations mean value theorum for integrals: \int_a^{b} f(x)dx=f(c)(b-a) mean value theorum for...
  33. U

    What Size Squares Should Be Cut to Maximize the Volume of a Candy Box?

    Homework Statement I remember doing something very similar to this in pre-calc, but I don't know where to get started. A candy box is to be made out of a piece of cardboard that measures 8 by 12 inches. Squares of equal size will be cit out of each corner, and then the ends and sides will...
  34. B

    Doppler Effect and absolute simultaneity

    The Doppler shift formula relates two proper time intervals measured in I and I' respectovely (tau)=D(tau)' D representing a Doppler factor that depends on the relative speed of I and I'. By definition the events involved in I and I' respectively take place at the same point in space. If the...
  35. B

    Can two stars have the same apparent but different absolute magnitudes

    Can two stars have the same apparent magnitudes but different absolute magnitudes? what about if two stars have the same absolute magnitudes but different apparent magnitudes?
  36. S

    Typo in Real Analysis Study Page: Absolute Value of x for x<0?

    I found a study page which lists the absolute value of x for x<0 as -x. I think this has to be a typo. The study area is real analysis. Does anyone have better information? Maybe it is some special notation?
  37. J

    Relativity: Absolute Acceleration & the Twin Paradox

    It seems to me that all of the talk about "absolute" acceleration is a complete non-issue, in terms of relativistic effects. For, if there is no such thing as absolute position, then there can be no such thing as absolute change in position, whether this change is understood in the sense of...
  38. R

    Can an Alternating Series Converge Absolutely?

    If \sum x_n converges absolutely, and the sequence (yn) is bounded, then the sum \sum x_n y_n converges. Find a counterexample that shows this isn't true when \sum x_n is conditionally convergent. I'm honestly not to sure where to begin with this one. I was thinking Monotone Convergence...
  39. B

    Solve Absolute Simultaneity with Einstein's Procedure

    Consider please the Lorentz transformation for the time coordinates of the same event t'(E)=g(t(E)-Vx/cc) (1) where g stands for gamma and t(E) and t'(E) for times displayed by clocks synchronized following Einstein's procedure. My question is: with what times displayed by how...
  40. S

    Equation and Inequation With Absolute Value [12th Grade]

    Homework Statement Resolve these equations and these inequations with the absolute values. Give the solutions in the form of interval : |2-x|< 4 |6-2x| = 3 |x+2| > 3 |4x²-12x+9| = 4 |3x+1|+|1-x|>3 |1-x²|=2x |x+2|<|x+3| |x^3-1|+pi[tex]>[tex]\sqrt{3} 3<|x+2|<4...
  41. F

    Series Convergence: Determining Absolute Convergence with the Squeeze Theorem

    Homework Statement Determine whether the series is absolutely convergent, conditionally convergent, or divergent. summation [cos((n)pi)/3] / n! from 1 to inf Homework Equations convergence tests The Attempt at a Solution I tried using the ratio test but that was ineffective since I...
  42. P

    Solving an Absolute Value Inequality with Two Terms

    Homework Statement \left|x-5\right|\leq\left|x+3\right| i know how to slove abs inequalities when there is one. like \left|x-5\right|\leq5. put x-5 between 5 and -5. then solve for x. i don't know how to start this. can someone provide some insight.
  43. P

    Absolute Extrema of 2x - (x-2) on [0,1], [-3,4]

    {} these brackets are going to represent the absolute value lines the problem states find the absolute extrema of the given function on each individual interval: f(x)= {2x} - {x-2} a) [0,1] b) [-3, 4] I know I need the derivative of the equation but it does not really give a good...
  44. K

    Exploring Absolute Zero and Its Impact on Time: A Theoretical Perspective

    (i have next to no knowledge about physics so please don't beat me down my there are flaws in my theories) as they say, time is defined by movement. you might say, "my eraser is perfectly still in my freezer (why you would put it there is beyond my comprehension)" be we are still moving on...
  45. B

    Can motion be detected without external reference in a moving container?

    Set-up #1: A person is enclosed in a container traveling with a constant velocity in the x direction. Wouldn't a laser inside the container attached to the floor and aimed perpendicular to the direction of travel (i.e., y direction) illuminate a spot on the ceiling of the container that is...
  46. S

    How can I prove the statement |a-b| < |a| + |b| using the triangle inequality?

    Homework Statement a and b are real numbers. Show l a-b l < l a l + l b l Homework Equations Well, I know la+bl < lal + lbl by the triangle inequality. The Attempt at a Solution If I can prove that la-bl < la+bl, then I'm done, but that most recent inequality almost seems...
  47. S

    Absolute Value Proof (Need Help)

    Homework Statement Prove that abs(a+b+c) is less than or equal to abs(a)+abs(b)+abs(c) Homework Equations None The Attempt at a Solution This makes sense to me that this would always be true, but i just can't seem to figure out how to write it out
  48. F

    What Does the Solution Set for |x² - 4| < 1 Look Like?

    Hello, abs(x^2 - 4) < 1 implies that: x^2 - 4 < 1 and 4 - x^2 < 1 solving first equation for x gives: -sqrt(5) < x < sqrt(5) solving second equation for x gives: -sqrt(3) < x < sqrt(3) Now, my question is, what does that mean?? How do I give the solution set, without a...
  49. L

    Why Do Solutions Sometimes Differ from Absolute Values?

    In equations dealing with absolute value sometimes the answer to the equation does not coorospond with the absolute value. Why is this?
  50. P

    What is absolute body temperature?

    I recently, read the "absolute body temperature" concept, but can't remember what was it, exactly. Can somebody help?
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