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. B

    Why is the absolute value of 16 not equal to 4?

    If ##\sqrt{x^2} = |x|##, why ##\sqrt{16} ≠ |4|## instead of 4 (please see below image)?
  2. barryj

    How to solve absolute value equation with two absolute values

    How does one solve an equation with two absolute value functions as below My algebra book does not show how to solve with two abs functions. 2|4x-1| = 3|4x+2| I thought this might work.. |4x-1|/|4x+2| = 3/2 then |(4x-1)/(4x+2)| = 3/2 and solve the normal way..
  3. G

    MHB Sketching absolute value graph

    Sketch the region in the plane consisting of all points (x,y) such that |x-y|+|x|-|y|<=2
  4. Gaz

    Determine Absolute Speed Using Time Dilation

    So if time dilation is what's left after correcting for the optical effect and we want to know our motion through the universe. We can't use light because we have no reference point to what not being in motion is and there's lots of attempts using light which doesn't work. Why don't we just take...
  5. D

    Why is QFT insensitive to absolute energies?

    In the canonical formulation of QFT (to which I've been exposed), it is always argued that only differences in energy are physically observable and so we can deal with the fact that the vacuum energy is infinite by redefining the vacuum such that its energy is zero and we subsequently measure...
  6. D

    Why is Gravity Sensitive to Absolute Energy?

    As far as I understand it gravity is sensitive to absolute energies, as seen directly through Einstein's equation G_{\mu\nu}=8\pi GT_{\mu\nu} Thus the local geometry of spacetime is directly affected by the local energy density (and not just differences in energy). So whenever gravity is taken...
  7. E

    Conservation of energy in a moving frame

    I know a similar question has been asked but I'm still kind of stumped. Imagine the Earth on the left and a small mass to it's right separated by some distance h. You are in the frame of reference where the Earth and the small mass are moving to your right at some speed v. So, both the Earth...
  8. Dong Aleta

    When to use absolute or gauge pressure in computations

    Hi! One of our professors told us once that in solving problems, always use absolute pressure in the computations. Then one time, I was solving some problems from Dr. Felder's Principles of Chemical Processes book, I often noticed that the pressures used in computations were not always in...
  9. P

    Definite integral of an absolute value function

    Can we integrate: $$\int_a^b |x| dx$$ using an antiderivative of ##|x|##, namely ##\frac{1}{2} x |x|##, instead of splitting up the integration interval? I know this is not particularly useful for integrals such as: $$\int_{-5}^5 |t^3 - 8| dt$$ However, for absolute value functions with linear...
  10. Dishsoap

    Schools Grad School Admissions - comparative or absolute?

    Greetings all, I found some similar threads to this but none that answered my exact question. I am doing an REU at a school I would like to attend for graduate school, and some students there have said that in graduate school admissions, I am going to be judged relative to my peers from the...
  11. Y

    Is absolute count of emission spectrum meaningful?

    I am using Renishaw confocal Raman microscope to do photoluminescence spectroscopy of some polymer inside microchannel. When I fix the laser power and exposure time, the absolute count of intensity will change from time to time even for the same sample. I was hoping the intensity should linearly...
  12. evinda

    MHB Calculations - absolute stability

    Hello! (Wave) The following Runge-Kutta method is given. $$ \begin{array}{c|ccccc} \tau_1 =0 & a_{11}=0 & a_{12} = 0\\ \tau_2 =\frac{5}{2} & a_{21} = \frac{5}{2} & a_{22} = 0\\ \hline & b_1 = \frac{4}{5} & b_2 = \frac{1}{5} & \ \end{array} $$ I have to determine the order of accuracy and...
  13. evinda

    MHB Find Stability for Euler Method: Absolute Stability of Second Order ODE

    Hello! (Wave) I am looking at the following exercise.We suppose that the explicit Euler method is applied at the differential equation of second order $\left\{\begin{matrix} x''(t)+(\lambda+1)x'(t)+ \lambda x(t)=0\\ x(0)=1\\ x'(0)= \lambda-2 \end{matrix}\right.$ $$|\lambda|>>1$$ What step...
  14. D

    Dynamics: Absolute and Relative Acceleration in Plane Motion

    Homework Statement A force P is applied to the rod which rests on a horizontal table. The following accelerations are produced. aA= 3.6m/s2 to the right, α of the rod = 6 rad/s2 CCW. Determine the acceleration of point G and B Homework Equations aG=aA+aG/A aG=aA+[(aG/A)tangential +...
  15. ORF

    Absolute Temperature & Entropy: Which is Lorentz Scalar?

    Hello In relativity, what magnitude is absolute*: temperature or entropy? *absolute = equal for all observers (= a Lorentz scalar) Thank you for your time :) Greetings!
  16. Samurai44

    Calculating Critical Angle: Relative vs. Absolute Refractive Index

    Greetings, Do we use Absloute refractive index when finding crtical angle ? if it was two mediums ( not vacuum or air) how would i calculate the critical angle ? I mean i get confused when I find relative refractive index because sometimes i get sine inverse greater than 1 which give no...
  17. ShayanJ

    Negative absolute temperatures - Comments

    Shyan submitted a new PF Insights post Negative absolute temperatures Continue reading the Original PF Insights Post.
  18. Walteholic

    Will absolute zero change with pressure?

    Say we are talking about an ideal gas. According to ideal gas law (PV=nRT), assuming the gas is now at absolute zero, if we further decrease the pressure of the environment, while keeping the container volume constant, will the gas goes under absolute zero? I wasn't an expert in Physics so...
  19. shanepitts

    Is My Approach to Finding Absolute Magnitude Correct?

    Homework Statement [/B]Homework Equations m1-m2[/SB]=2.5log(ι2/ι1) m-M=2.5log (d/10)2 3. The Attempt at a Solution Not sure if my approach and answers are correct Please help
  20. PsychonautQQ

    Integral of absolute value function

    how do i evaluate say a definite integral from [-3,3] of |x+1|? Any advice? I'm so confused.
  21. shanepitts

    Why is the absolute value only in the numerator here?

  22. K

    MHB Absolute Value of Complex Integral

    Let $[a,b]$ be a closed real interval. Let $f:[a,b] \to \mathbb{C}$ be a continuous complex-valued function. Then $$\bigg|\int_{b}^{a} f(t)dt \ \bigg| \leq \int_{b}^{a} \bigg|f(t)\bigg| dt,$$ where the first integral is a complex integral, and the second integral is a definite real integral...
  23. W

    Is it possible to achieve absolute zero?

    Is it possible to achieve absolute zero?
  24. evinda

    MHB Region of absolute stability

    Hello! (Wave) We have the problem $$\left\{\begin{matrix} y'=\lambda y &, t \in [0,+\infty), \lambda \in \mathbb{C}, Re(\lambda)<0 \\ y(0)=1 & \end{matrix}\right.$$ Applying the Backward Euler method $y^{n+1}=y^n+h \lambda y^{n+1}$, we get that $y^n=\frac{1}{(1-h \lambda)^n}$. So that the...
  25. J

    Absolute pressure, buoyant force, tension problem

    Homework Statement A diving sphere has a mass of 150,000.0kg and an external diameter of 7.000 meters. The sphere is anchored with a cable on the bottom of an ocean, at a depth of .8000 km. The density of sea water is 1025.0kg/m3. A) What is the absolute pressure at that depth in pascals? B)...
  26. binbagsss

    Valence Tensor of "DVu/Du" Acting on Vector: Analyzing 1 to 1

    Acting upon a vector say, so it is defined as: ##\frac{d}{d\lambda}V^{u}+\Gamma^{u}_{op}\frac{dx^{o}}{d\lambda}V^{p}=\frac{DV^{u}}{D\lambda}## And this can also be written in terms of the covariant derivative, ##\bigtriangledown_{k}## by ##\frac{DV^{u}}{D\lambda}=\frac{d x^{k}}{d \lambda}...
  27. R

    Absolute magnitude and luminosity

    Do two stars of the same absolute bolometric magnitude have the same absolute visual magnitude? If this is true; does this mean that two stars with the same power output have the same have the same bolometric magnitude and therefore same visual magnitude?
  28. R

    Difference in power and absolute magnitude of a star

    My physics book mentions that a stars luminosity is its total power output at all wavelengths and that absolute magnitude is defined as inherent brightness and NOT luminosity. It then mentions that two stars of the same power output have the same absolute magnitude. Since luminosity is the...
  29. anemone

    MHB What is the minimum value of y in the Absolute Value Function?

    Determine the minimum of $y$ where $y=|x-1|+|2x-1|+|3x-1|+\cdots+|nx-1|$.
  30. R

    A definite trigonometric absolute integral

    Homework Statement Find ## \int_0^{nπ+v} |sinx| dx ## Options are, 2n+ 1+ cosv 2n+1-cosv 2n+1 2n+cosv Homework Equations Integration of sinx is -cosx.The Attempt at a Solution Sin x is + ve from 0 to π, Negative from π to 2π We can make |sinx| as sinx in 0 to π, And - sinx in π to 2π But here...
  31. P

    Limits involving absolute values

    This is actually a physics problem, but since my question is really about the math involved, I decided to post it in the calculus subforum. I'm supposed to get from the term: $$\lim_{\Delta t → 0} |\vec{v}_r (t + \Delta t)| \frac{\sin \Delta \theta}{\Delta t}$$ To: $$v_r (t) \frac{d\theta}{dt}$$...
  32. A

    Teacher told to set absolute value inequality to equal 0

    So I was helping my sister on homework and there was this problem: 2 abs(2x + 4) +1 > or equal to -3 teacher told her to ignore the -3 and just set it equal to zero. Soo should you? This question got me confused. can't you just go about solving, bringing the 1 to the left and then dividing by 2...
  33. evinda

    MHB What Defines the Regions of Absolute Stability in Numerical Methods?

    Hello! (Wave) We have to look for numerical methods for the numerical solution of $\left\{\begin{matrix} y'(t)=f(t,y(t)) &, a \leq t \leq b \\ y(a)=y_0 & \end{matrix}\right.$ that have 'great' regions of absolute stability. Methods of which the region of absolute stability contains the whole...
  34. P

    Differentiability of the absolute value of a function

    The derivative of ##|f(x)|## with respect to ##x## is ##f'(x)## for ##f(x) > 0## and ##-f'(x)## for ##f(x) < 0##. However, it is undefined wherever the value of the function is zero. I was wondering, though, if the product of this "undefined derivative" and zero is zero.
  35. Mr Davis 97

    Question on logarithmic differentiation and absolute value

    For the problem of differentiating ##y = x^5(3x-1)^3## using logarithmic differentiation, the solution provides the first step as rewriting the functions as ##\left |y \right | = \left | x \right |^5 \cdot \left | 3x-1 \right |^3##. This confuses me. First, how are we, mathematically, able to...
  36. anemone

    MHB Is the Absolute Value Inequality $|4x-5|-|3x+1|+|5-x|+|1+x|=0.99 Solvable?

    Show that the equation $|4x-5|-|3x+1|+|5-x|+|1+x|=0.99$ has no solutions.
  37. patrickbotros

    Absolute Values in Separable Differential Equations

    When solving a separable differential equation, my textbook says this: ln|v-49|=-t/5+C→ |v-49|=e-t/5+C→ v=49+ce-t/5 What happened to the absolute values? I think it has something to do with the exponential always being positive.
  38. T

    Will This Method Yield Absolute Synch?

    -simple procedure designed to absolutely synchronize clocks- Picture the face of a very large clock with a one hand. Let's place a small clock A at the 9 o'clk position of the large clock, and let's place another small clock B at the 3 o'clk position. We use clock A to time the large clock's...
  39. gfd43tg

    Absolute value of exponentials being multiplied

    I know this is an elementary question, but it has been some time since I multiplied exponentials, and with imaginary terms combined with absolute values, things get muddled up so easy that I want to clear this up So if I have $$ \Psi (x,t) = c_{1} \psi_{1} e^{- \frac {i E_{1}}{\hbar} t} +...
  40. J

    In absolute need of help with chemistry labs

    I just got out of my chemistry lab class at school, and needless to say, I don't think I am going to get a good grade. Basically, I felt like a complete idiot today. My professor was getting frustrated with me because he thinks I wasn't listening to him (even though I was). I never in my life...
  41. A

    High conductivity materials in absolute temperatures

    what happen to the conductor if it reaches the critical temperature where high conductivity and then back to the original case does it preserve by an amount of high conductivity or high conductivity disappear just a question I'm engineering student electrical power department
  42. DaveC426913

    Absolute Hot - infographic on temperatures

    Just stumbled across this on my favorite site Dark Roasted Blend: I did not know there was an 'absolute hot'. (it's too large to post here) http://i.imgur.com/iHW7Dwh.png
  43. M

    Designing a Circuit to Return Absolute Value of 3-bit Number

    Homework Statement Make the design of a circuit returning the absolute value of a number of 3 bits . The input and output must be signed , use the complement 2. Show your approach and draw your track using logic gates. I seriously do not understand this at all. What am I supposed to do...
  44. J

    What is the significance of U at infinity in relation to Earth?

    hello sir ...can anyone explain me the value of (U) at infinity with respect to Earth as reference point
  45. F

    MHB Does e^{2 \ln{|x|}} = |x^2| or x^2?

    is e^{2 \ln{|x|}} = |x^2| or x^2?
  46. psuedoben

    Do we have any idea what would happen at theoretical absolute zero?

    i have a simple question, but I'm not sure it can be answered with our knowledge of absolute zero: if an object were to exist at absolute zero, that means it has no energy, correct? if that is true, then if you struck something at absolute zero with another object, would the object with no...
  47. S

    Absolute magnitude of the sun.

    1. (a) What is the distance modulus of the Sun? (b) What is the Sun’s absolute magnitude?2. I found the distance modulous using 5log(4.84E-6/10) to be -31.6. I feel like I need the apparent magnitude to get the absolute, my teacher is very vague about what we are given to use. Is there a way...
  48. K

    Dew point and absolute humidity

    Homework Statement Room temperature is 200C and relative humidity is 60%. what is the absolute moisture Homework Equations Vapor pressure at 200C=17.5[atm] PV=nRT Molecular weight of water=18[gr/mol] The Attempt at a Solution The vapor pressure at 200C: $$\frac{x}{17.5}=0.6\rightarrow...
  49. S

    MHB Absolute Value with two expressions.

    How do I do this? I have tried a few methods and end up getting x values that don't work when placed back into the equation.
  50. jacobi1

    MHB Trigonometric absolute value integral

    Evaluate \lim_{n \to \infty} \int_0^1 | \sin(nx)| \ dx.
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