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. N

    Solving absolute value inequalities

    Homework Statement [abs(x)]/[abs(x+2)]<2 Homework Equations The Attempt at a Solution case 1: [abs(x)]/[abs(x+2)]<2 case 2: [abs(x)]<2[abs(x+2)] is this right so far? if so, why is there two cases and what do i do next?
  2. C

    Atoms at Absolute 0: Subatomic Kinetic Energy

    Atoms at "Absolute 0" Hi everyone, I'm in high school right now so sorry if this question seems stupid or blatantly obvious to most of you, but at absolute zero, I understand atoms in a material cease to move and lose all kinetic energy between atoms, but what about the atom on a subatomic...
  3. A

    How to interpret absolute value bars?

    I was further looking into the Cauchy schwarz inequality and i got to a statement as follows: A·B ≤ |A·B| However, when I tried to prove this using numbers on paper, I wasn't sure if the absolute value bars distribute among each term, which would lead to |A|·|B|, or if the final product is...
  4. R

    Absolute Derivative: Proving Vector Field Along ##\gamma##

    Homework Statement Please show that the absolute derivative is a vector field along ##\gamma##, i.e., ##(\frac{d\lambda ^{a'}}{du}+\Gamma^{a'}_{b'c'}\lambda^{b'}\frac{dx^{c'}}{du})=X^{a'}_d(\frac{d\lambda ^{d}}{du}+\Gamma^{d}_{ef}\lambda^{e}\frac{dx^{f}}{du})## The Attempt at a Solution I...
  5. Dale

    The terms absolute and relative

    The terms "absolute" and "relative" In discussions about relativity I use the term "absolute" as a synonym for "frame invariant" and "relative" as a synonym for "frame variant". I went to look for an authoritative definition and could not find one, so I am a little concerned. Is my usage...
  6. A

    Solving absolute value equations

    Is this a correct a way of thinking for solving absolute value equations? Say I have |2x+6|-|x+3|=|x| and want to solve for x, then I have: For |2x+6| 2x + 6 if x ≥ -3 -2x - 6 if x < -3 For |x+3| x+3 if x ≥ -3 -x-3 if x<-3 For |x| x if x ≥ 0 -x if x < 0 Am I supposed to look at...
  7. G

    Possible Value(s) for X in |x-3| = -2?

    The equation |x-3|=-2 is given. Find the possible value(s) of X. I don't understand how it could equal a negative number but here is my weak attempt. |x-3|= -2 -|x-3|= 2 -x+3=2 -x=-1 x=1 I substituted x=1 into the equation and all I got was 2 as the answer. Any help would be...
  8. A

    Is acceleration relative or absolute?

    I don't mind according to whose mechanics like einstein or Newton but what exactly is acceleration truely..If 2 bodies accelerating at same speed,then do the first body appear stationary for second and viceversa or is there any fictious force acting on them..?
  9. T

    Absolute Value and Converting to Expanded Form: Explained

    Just a general question with absolute values: Is it possible to have an absolute value of this form: | f(x) - L | < -L (the minus sign is meant to be there) and if so how can I convert it into expanded form? i.e: -L < f(x) - L < -L or something of that form.
  10. V

    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...
  11. M

    Absolute value definite integral

    Homework Statement ∫[|2x-1|] evaluated on the interval [1,-1] Homework Equations The Attempt at a Solution I know we must split it into two equations ∫ from [a,c] + ∫ from [c,b] and in absolute value one is negative and one is positive, so it will be 2x-1, and 1-2x my...
  12. A

    How to solve a system of linear inequalities with absolute magnitudes?

    Hi everybody, I'd love to pick your brains about a problem in (seemingly?) linear algebra I've run into, trying to find the most efficient algorithm for solving a set of linear inequalities involving absolute magnitudes. During my research I've run into a problem that involves solving a...
  13. Q

    Can Absolute Velocity be Measured?

    Just a silly idea i have, please debunk it since i cannot figure it out: The Thought Experiment: Provided to us is a spacecraft equipped with a particle acceleration and detection systems. The craft is set on a course where it would not be interrupted by any interstellar objects and...
  14. N

    Sense of Absolute in Relativity?

    This could be very basic question, nevertheless its troubling me In Feynman's lectures, he says that though motion is relative, there is an absolute motion between 2 frames. A high velocity mu-meson when moved linearly or circularly would live just as longer than stationary one. Or a twin in a...
  15. Q

    Integrating Square Roots - Absolute Value Needed?

    Homework Statement http://i.minus.com/i61zvy2BbtqkI.png Homework Equations One can factor the polynomial to (x-1)^2 The Attempt at a Solution After factoring the polynomial, I integrate (x-1) given the bounds of 0 and 1. I get -1/2. The solution manual says the answer is...
  16. M

    Beyond Absolute Infinity, then neither Beyond nor not beyond

    What is beyond Cantor absolute infinity? Then can you imagine what is neither beyond nor not beyond, which is we can't even say that 'the Being is beyond the universe or beyond infinity' to that particular Being? And what is neither singular/oneness nor multiplicity?
  17. R

    Exploring the Concept of Absolute Maximum Temperature

    Like absolute zero, is there an absolute maximum temperature?
  18. J

    Absolute value removed from equation. Why?

    Homework Statement Given that \epsilon> 0, why is it, that \left | x_{n} -L\right |< \epsilon implicates that x_{n} > L-\epsilon ? Homework Equations The Attempt at a Solution
  19. L

    Absolute and conditional convergence of series (1 + x/n)^n^2

    Homework Statement \sum from n=1 to n=\infty (1 + \frac{x}{n})n2 Determine the values of x for which the series converges absolutely, converges conditionally and diverges.The Attempt at a Solution So i tried using the root test for the absolute value of (1 + \frac{x}{n})n2, but it was...
  20. M

    What Factors Affect Absolute Pressure at Lake Depths?

    Homework Statement Calculate Absolute Pressure? (1) A Lake has average temperature of 10°C and a maximum depth of 35m. The barometric pressure at the lake is 598mmHg. At the deepest part of the lake, determine the absolute pressure in Pascals. Specific weight of the water in the lake...
  21. C

    Linear programming with absolute value objective function

    Homework Statement Minimize |2x1-3x2| subject to x1+x2≤5 -x1+x2≥-1 x1≥0, x2≥0 (a) Solve the problem graphically. (b) Formulate a linear program that could be used to solve the problem. Use software to solve your LP and show how to reconstruct a solution to the original problem...
  22. 9

    Find the absolute maximum for f(t) = -t^3 + 3t^2 + 400t + 5000

    Homework Statement Find the absolute maximum for f(t) = -t^3 + 3t^2 + 400t + 5000, t is between 6 and 20. Homework Equations f'(t) = -3t^2 + 6t + 400 The Attempt at a Solution I know how to find this - when the function can be perfectly factored. Yet some problems occur here...
  23. Z

    What is the true nature of motion?

    I think the experiment of Newton's bucket is wrongly criticized.They deny the absolute velocity,it is right ,but they agnore the absolute nature of motion,which is not relative to other system,but is relative to the thing itself at the previous adjoining instant.Such as the expanding of universe...
  24. B

    Why does the half of the absolute value of a matrix formed with its coordinates give

    Why does the half of the absolute value of a matrix formed with its coordinates give the area of a triangle? I don't see any similarity between that and the heron's formula.
  25. alexmahone

    MHB Is the Series $\displaystyle\sum\frac{\sin n}{n}$ Absolutely Convergent?

    Using the fact that the interval $\displaystyle\left[2k\pi+\frac{\pi}{4},\ 2k\pi+\frac{3\pi}{4}\right]$ contains an integer, prove that $\displaystyle\sum\frac{\sin n}{n}$ is not absolutely convergent.
  26. alexmahone

    MHB Absolute Convergence: Proving $\sum a_n$ is Convergent

    Prove that if $\displaystyle \left|\frac{a_{n+1}}{a_n}\right|\le\left|\frac{b_{n+1}}{b_n}\right|$ for $\displaystyle n\gg 1$, and $\displaystyle\sum b_n$ is absolutely convergent, then $\displaystyle\sum a_n$ is absolutely convergent.
  27. L

    Limits & derivative of absolute value of x

    For absolute value of x, f(x) = lxl To prove continuous, I can express it as a piecewise function of x if x>0 and -x if x<0 and then I can take the limit of each as x approaches 0 from the negative and positive sides. Both limits give zero, and f(0) gives zero, so continuity is...
  28. alexmahone

    MHB Subsequence - absolute convergence

    Let $\{a_n\}$ be a sequence, and $\{a_{n_i}\}$ be any subsequence. Prove that if $\sum_{n=0}^\infty a_n$ is absolutely convergent, then $\sum_{i=0}^\infty a_{n_i}$ is absolutely convergent. My attempt: $\sum |\ a_n|$ is convergent. $b_n=\left\{ \begin{array}{rcl}|a_{n_i}|\ &\text{for}& \...
  29. U

    Magnetism seems absolute despite being relativistic effect of electrostatics

    I know that magnetic force due to a current carrying wire on a test charge moving w.r.t the wire(along the wire), can be interpreted as the electrostatic force if we use the first order relativistic corrections for Time Dilation or Length contraction of the charges of the wire, in the frame of...
  30. V

    Complex conjugate of absolute exponential

    Hello all, I am trying to figure out how to solve for the complex conjugate of the following: (-0.5)^abs(x) Thanks for your help. -Brian
  31. V

    (Tricky) Absolute Value Inequalities

    Hello everyone, I'm posting here since I'm only having trouble with an intermediate step in proving that \sqrt{x} \text{ is uniformly continuous on } [0, \infty] . By definition, |x - x_0| < ε^2 \Longleftrightarrow -ε^2 < x - x_0 < ε^2 \Longleftrightarrow -ε^2 + x_0 < x < ε^2 + x_0 1...
  32. T

    Absolute Value of Limits Proof

    Homework Statement Show that if bn→b, then the sequence of absolute values |bn| converges to |b|. Homework Equations The Attempt at a Solution I've been proving various properties of limits, including product of limits and sum of products, but have been having trouble making...
  33. Saladsamurai

    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| <...
  34. karush

    MHB Inequality with absolute value

    Write as one inequality with an absolute value x<-5 or 8<x not sure how you introduce the absolute value in this to solve it. thanks ahead
  35. A

    Integration Problem involving absolute bracket, sine,cosine

    Homework Statement Evaluate ∫(1)to(-1) l sin(x) l dx Homework Equations The Attempt at a Solution If I just leave it like this, is it wrong? 1. ∫(1)to(-1) l sin(x) l dx = l -cos (x)l 2. l -cos (1) l — l -cos (-1)l = 0 - 0 = 0
  36. E

    F(f(x)) when f(x) = absolute value of x-1

    Homework Statement Suppose f is the function defined by f(x) = l x-1 l Sketch the graph of y = f(f(x)) Homework Equations The Attempt at a Solution It's not so much sketching the graph that is the problem as much as it is figuring out how to set up the equations. How do I put an...
  37. C

    Absolute Magnitude Calculation, How?

    Hello everyone, Glad to be a new member of this superb forum :) In one of my physics classes, I have to construct an H-R Diagram. Now, this does not seems too challenging, and I'm sure it isn't. I was wondering if someone could kindly guide me in the right direction without giving me an...
  38. S

    Linear Differential Equation: Dropping Absolute Value Bars

    I'm doing some practice problems, and with the help of my solutions manual and wolfram alpha I've worked out a solution to (x+1)\frac{dy}{dx} +xy = e^{-x} However, I don't understand why we can drop the absolute value bars when we calculate the integrating factor: e^{\int...
  39. A

    How Do You Calculate the Absolute Uncertainty of One Rotation Time in a Dryer?

    Homework Statement Lab 1: Question 6. (Note: each time you do this problem, the numbers will be different.) I want to measure accurately the time it takes for the drum of my clothes dryer to make one rotation. Since the door on the dryer is made of heat resistant glass, I can see the...
  40. H

    Contour integral with absolute value

    Suppose I want to compute tthe integral: \int_{-\infty}^{\infty}\frac{\textrm{sech}\hspace{0.1cm} x}{x^{2}-2|x|+1}dx Can I compute this integral via contour integration? The only way that I have thought of is to split up the domain: \int_{-\infty}^{\infty}\frac{\textrm{sech}\hspace{0.1cm}...
  41. The Chaz

    MHB Limits Involving Absolute Value: Solutions & Explanations

    Let f(x) = |x|/x a. What is the limit of f, as x approaches 0 from the right? b. What is the limit of f, as x approaches 0 from the left? c. Hence, what is the limit of f, as x approaches 0? ------------------------------ The best way to evaluate limits involving absolute values is to use...
  42. N

    The Dirac delta in squere root of the absolute value

    Dear Forum Users, I have got more math question rather then the physics question. Does someone know if: \mid d(x)\mid^2 equals just d(x), here d(x) is just the Dirac delta ? best regards, nykon
  43. A

    Limit of Absolute Values: Understanding the Concept

    Homework Statement http://www4c.wolframalpha.com/Calculate/MSP/MSP621a026b7befdf1f1d00003b707661e1i20i4e?MSPStoreType=image/gif&s=55&w=126&h=38 Homework Equations limit x->3- (3x-9)/((abs(3x-9))The Attempt at a Solution I don't understand how to find the limit of absolute values..
  44. JJBladester

    Pressure in a manometer - Absolute pressure

    Homework Statement Consider the manometer in the figure. If the specific weight of fluid A is 100kN/m3, what is the absolute pressure, in kPa, indicated by the manometer when the local atmospheric pressure is 90kPa? http://www.composmentisconsulting.com/2-61.jpg Homework Equations...
  45. A

    Fiber Optics - Absolute and decibel Power Gains

    Homework Statement Problem is very simple but the textbook used for this class is complete garbage and has confused me to no end. a) Convert the following absolute power gains (dBm) to decibel power gains (dB). 10^-3 dBm, 2^n dBm b) Convert the following decibel power gains (dB) to...
  46. R

    Is Mass the Absolute Frame of Reference in the Universe?

    As stated in SR, mass of the object increases with its velocity right? Lets assume that all the objects in the universe have consciousness and they all know what their rest mass is...(Leave photons out of the argument).. And also assume they all can measure their own mass at any instant...
  47. J

    Trig identity with natural logs and absolute value?

    Trig identity with natural logs and absolute value?? Homework Statement -ln|csc(x) + cot(x)|= ln|cscx(x)-cot(x)| Homework Equations The Attempt at a Solution I got that csc(x)=1/sin(x) and cot(x)=cos(x)/sin(x), giving me a common denominator, added together I have...
  48. E

    Is there an absolute motionless?

    So I do not have a clue whether this question has any merit or not. (which is why I came here) I have heard that masses create ripples in space-time (gravity waves) as they move. I have drawn a couple of logical conclusions that I would appreciate if you guys would verify or discredit...
  49. T

    Writing an absolute value function as a piecewise function

    Homework Statement Write f(x) = |x2-x-12| as a piecewise function. Homework Equations The Attempt at a Solution -x2+x+12 where x>1/2 x2-x-12 where x\geq0 According to the answer book the answers are -x2+x+12 where -3<x<4 x2-x-12 where x\geq4 2x2-5x-3, x\leq1/2 I am...
  50. phosgene

    Absolute pressure of air inside a meat baster

    Homework Statement A meat baster consists of a flexible bulb attached to a plastic tube as shown in the diagram. When the open end of the tube is immersed in the basting sauce and the bulb is squeezed then released, sauce rises in the tube so that it can be squirted over the meat. Suppose...
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