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. P

    Solving absolute values of trigonometry

    Homework Statement Homework EquationsThe Attempt at a Solution 2sin3x=1 OR 2sin3x= -1 sin3x=1/2 sin3x= -1/2 From the unit circle and in accordance with the domain there are 3 solutions (B) But the answer is (C) HOW?
  2. Matthew Bristow

    Can the speed of light be constant and absolute?

    Hi all I have struggled with the assumptions that the speed of light is absolute and constant. I have some logic to this which is based on the common assumptions that light behaves both as a wave and a particle. It is also based on light having mass, the effects of heat and vacuum environments...
  3. M

    B Testing spacetime collapse at absolute zero

    The other day I was pondering what happens at/near absolute zero so I did some googling and found articles talking about how it has been demonstrate that as you near absolute zero, the quantum effect start to have an increased range. However, is seems that perhaps the quantum effects only get...
  4. R

    B Absolute Movement and Time in 3D Space: Exploring the Relationship

    if you have 3 space ships on the x, y and z axis and they blast off...one of them must be moving in an absolute sense. Is it the case that if there is absolute movement then there MUST be absolute time also?
  5. Jonforall

    Must we always use absolute value for lens magnification?

    My brother's physics teacher says that magnification and height of image are always positive. Is she right?
  6. Jordan M

    Theoretical ξr of a molecule from the absolute configuration

    I am wondering if anybody knows how to calculate the theoretical relative permittivity of a molecule (1) using the theoretical configuration and values that are easily accessible (2). I am also wondering what the technique would be. In my pharmaceutical reaction class and also O-chem 2 we have...
  7. M

    MHB Convergence of Alternating Series and Estimation of Absolute Error

    Hey! :o I want to determine the value of $n\in \mathbb{N}$ such that the absolute error $$\left |\sum_{k=0}^{\infty}\frac{(-1)^k}{(2k+1)\cdot k!}-\sum_{k=0}^{n}\frac{(-1)^k}{(2k+1)\cdot k!}\right | =\left |\sum_{k=n+1}^{\infty}\frac{(-1)^k}{(2k+1)\cdot k!}\right |$$ is less than $10^{-6}$. Do I...
  8. D

    What is the mistake in calculating the integral of the absolute sine function?

    Homework Statement \int_0^{2018 \pi} \lvert \sin(2018x) \lvert \mbox{d}x Homework EquationsThe Attempt at a Solution So the period is: \frac{2 \pi}{ 2018} Each "hump" of the sine has an area of 2 so if I count the number of humps I am done. In one period of an absolute sine function the...
  9. RabbitWho

    I Odds ratio and percentages.... absolute beginner

    Imagine that the chances in the USA of adult men having GAD are on average 1 in 100. But what of the subset of adult men who already have MD? What are the chances that such men will have GAD as well as MD? An odds ratio tells us about the increase in the chance that such men will have GAD...
  10. mishima

    B Absolute Value Inequality, |x|>|x-1|....where's my mistake?

    Rule: Suppose a>0, then |x|>a if and only if x>a OR x<-a So |x|>|x-1| becomes: x>x-1 which is false (edit: or more accurately doesn't give the whole picture, it implies true for all x) OR x<-x+1 2x<1 x<1/2 which is false
  11. H

    How to solve this integral of an absolute function?

    Homework Statement Homework EquationsThe Attempt at a Solution I think the answer for number 1 , graph somewhat like this I get trouble for 2, 3, etc I (k) = ##\int_{-1}^{1} f(x) dx ## f(x) = ## \mid x^2 - k^2 \mid## 2) k < 1 for negative side ##\int_{-1}^{-k} (x^2 - k^2) dx +...
  12. shivakumarvv75

    B Velocity of light and absolute rest

    dear sir, light travels with constant speed of 3 x 10^8 m/s. does that mean light is in absolute motion irrespective of the its source?
  13. M

    MHB Why can't real numbers satisfy this absolute value equation?

    Explain, in your own words, why there are no real numbers that satisfy the absolute value equation | x^2 + 4x | = - 12. Can we say there is no real number solution here? If so, is the answer then imaginary taught in some advanced math class?
  14. Oklid

    Question about Absolute Dependent Motion Analysis

    Homework Statement [/B] Find accelerations of these masses and the pulley are weightless. Homework Equations [/B] Sb+Sc=Length of the second rope (L2) The Attempt at a Solution [/B] Just like I did, I placed all variables from datum to the masses. In the second system, I write the...
  15. M

    I Comparing two absolute value equations

    Hello, How does one go about algebraically checking if |x+|y+z|| and ||x+y|+z| are equal?
  16. aquaelmo

    Find the cdf given a pdf with absolute value

    Homework Statement Consider a continuous random variable X with the probability density function fX(x) = |x|/5 , – 1 ≤ x ≤ 3, zero elsewhere. I need to find the cumulative distribution function of X, FX (x). 2. Homework Equations The equation to find the cdf. The Attempt at a Solution FX(x)...
  17. S

    B How to interpret the integral of the absolute value?

    This is rather basic, and may be a misconception of the notation, however, I can't make the following sum up: The following is given: x_n(t) = 1 -nt , (if 0 <= t <= 1/n) and 0, (if 1/n < t <= 1) However, this part I can't grasp this part in the book: \begin{equation} ||x_n||^2 = \int_0^1...
  18. C

    I Exploring the Limits of Density: Is There an Absolute Maximum?

    This is kind of a random question. Is there a point that a substance density will max out? Or in other words that it cannot be compressed any further no matter the energy you add to the system?
  19. J

    I Fermi gas at the absolute zero T

    I'm currently studying Thermodynamic properties of a Fermi gas at the absolute zero temperature. I get how the internal energy, pressure... etc of the gas are derived. For example, in computing the internal energy, one sums up all the energy of states weighted by its average occupation...
  20. C

    Absolute zero temperature is impossible to achieve?

    Just a general musing. Could absolute zero ever be physically possible or is it like the speed of light but for an inverse reason? The speed of light take infinite energy to achieve. So therefore is impossible because the energy put into the system adds mass. This is not noticeable at slower...
  21. K

    Work done by a force over a distance, relative or absolute?

    When we calculate the work done by a force applied on an object (suppose force and movement are in the same direction and a constant force) do we take into account the relative distance ot the absolute distance. When saying relative distance i mean if the object is moving on top of a platform...
  22. M

    MHB Absolute Value Equation

    Explain why there are no real numbers that satisfy the equation $$|x^2 + 4x| = - 12$$ How is this done algebraically?
  23. M

    MHB Absolute Value Definition....3

    Use the algebraic definition of absolute value to rewrite the expression below in a form that does not contain absolute value.
  24. M

    MHB Absolute Value Definition....2

    Use the algebraic definition of absolute value to rewrite the expression below in a form that does not contain absolute value.
  25. M

    MHB Absolute Value Definition....1

    Use the algebraic definition of absolute value to rewrite the expression below in a form that does not contain absolute value.
  26. M

    B Apparent magnitude / absolute magnitude / luminosity

    Hello, When we talk about the luminosity, apparent magnitude or absolute magnitude of a star, are we talking about all wavelengths of EM radiation or just a certain range? I've read that luminosity is basically the power output of all types of radiation, but the apparent magnitude scale is...
  27. EastWindBreaks

    Pressure reported from a water line, gauge or absolute?

    Homework Statement Homework EquationsThe Attempt at a Solution I thought the pressure in a water line is in gauge pressure, but the solution suggests that 1630 kPa is in absolute pressure, do we always assume absolute pressure unless otherwise specified?
  28. C

    Exploring the Absolute HOMO: Spectroscopy & Beyond

    What exactly is the absolute highest occupied molecular orbital? I think, as the name suggests, it's the absolute highest occupied molecular orbital in a molecule. Could it be determined using spectroscopy? Maybe, depending on the type. You could use UV-Vis if the energy gap between the HOMO...
  29. L

    I How is uncertainty affected by absolute numbers?

    Example: Say I want to calculate the evaporation rate of water and so I record the mass of some amount of water every 30 seconds for 5 minutes. The uncertainty in the scale is inherently .0001g and so that would be the uncertainty in the mass of any individual measurement, but how would I...
  30. K

    How to calculate : Mass flow of water vapor in the air (kg/h)

    Hello Homework Statement Lets say i have the given parameters: air volume flow : V = 36 m3/h Relative humidity: RH=33% air mixing ratio : X = 5.5 (1g H2O) / 1kg (DRY AIR) (calculated from RH) air temperature : T= 20 C So i know how much mass of water is the air compared to the air's "dry air"...
  31. U

    B Brainstorm: Is absolute zero relative

    I know that absolute zero is impossible to achieve but we can get close. According to google the coldest temperature ever reached in a lab was 0.006K. Do you think this is because while the atoms are moving very slow relative to the observer they are still moving at the velocity of Earth's...
  32. Another

    Testing Absolute Convergence of ∑(-2)n+1/n+5n

    ∑ (-2)n+1/n+5n Test this series Absolute Convergence ? ∑|an| = ∑(2)n+1/n+5n if the sum of |an| converges, than the sum of an converges ∑|an| = ∑(2)n+1/n+5n I can use Comparison Test? I can choose series bn = ∑ 2n/5n ?
  33. kalpalned

    Absolute value notation removal

    Homework Statement Rewrite |x| < 1 and |x| > 1 by eliminating the absolute value sign Homework Equations |x| < 1 = -1 < x < 1 |x| > 1 = ? The Attempt at a Solution I know that |x| < 1 can be rewritten as -1 < x < 1 but I'm not sure about |x| > 1. Am I right to assume that |x| > 1 = -1 > x > 1?
  34. karush

    MHB 232.q1.2c Double integral with absolute value in integrand

    $\displaystyle \int_{-1}^{1} \int_{-2}^{3}(1-|x|) \,dy\,dx$ ok i was ? about the abs
  35. M

    MHB Absolute Value Equation

    -3|x+5| + 1 = 7|x+5| + 8 Solution: -3|x+5| – 7|x+5| = 7 -10 |x+5| = 7 |x+5| = -7/10 x+5 = ±(-7/10) x = ±(-7/10) – 5 x₁ = -7/10 – 5 x₁ = -57/10 x₂ = 7/10 – 5 x₂ = 2/10 x₂ = 1/5 Correct?
  36. T

    Manometer finding absolute pressure at P1

    Homework Statement https://imgur.com/a/nxWvK this is the problem Homework Equations P=Patm + dgh The Attempt at a Solution I really just need to check if i did this right. I converted the densities to kg/m^3 and did p1= ((1121.689)(9.8)(.15) + ((1019.717)(9.8)(.04)) which gives 2048.61 Pa +...
  37. B

    B Solving Absolute Value Inequalities: How to Define Cases

    Hi there, I'm having trouble understanding this math problem: |x| + |x-2| = 2 The answer says its: 0<=x<=2 I understand you need different "cases" in order to solve this. For example, cases for when x is less than 0, when x-2 is less than 0, etc. Thanks, blueblast
  38. Math Amateur

    I Limits and Continuity - Absolute Value Technicality ....

    I am reading Manfred Stoll's Book: "Introduction to Real Analysis" ... and am currently focused on Chapteer 4: Limits and Continuity ... I need some help with an inequality involving absolute values in Example 4.1.2 (a) ... Example 4.1.2 (a) ... reads as follows: In the above text we read ...
  39. Math Amateur

    MHB Limits and Continuity - Absolute Value Technicality ....

    I am reading Manfred Stoll's Book: "Introduction to Real Analysis" ... and am currently focused on Chapteer 4: Limits and Continuity ... I need some help with an inequality involving absolute values in Example 4.1.2 (a) ... Example 4.1.2 (a) ... reads as follows:In the above text we read ...
  40. V

    How do I solve where the absolute potential should be zero?

    Homework Statement A point charge of + 2.0 μC is placed at the origin of coordinates. A second, of − 3.0 μC, is placed on the x-axis at x = 100 cm. At what point (or points) on the x-axis will the absolute potential be zero? Homework Equations V= ko*∑ (q/r) The Attempt at a Solution My work...
  41. MikeGomez

    I Did Newton Believe in Absolute Motion? A Closer Look at His Arguments

    An interesting subject that was getting off topic from another thread… https://www.physicsforums.com/threads/does-gravitational-time-dilation-imply-spacetime-curvature.919181/ Note: Newton was not alone in this. Rene Descartes stated that the problem with relative motion is that every particle...
  42. B

    I Fitting a line by minimizing absolute deviation

    Hey guys!. I need to use this method of minimization. The procedure to follow is explained here: http://es.tinypic.com/r/35mmtg0/9 However, I do not fully understand. What do I have to do? What I got from the paper is that I only have to minimize the equation 15.7.16, by using bisection. With...
  43. H

    Find the min and max value from absolute function?

    Homework Statement Homework Equations f ' (x) = 0 -> to find extreme pointThe Attempt at a Solution can I differentiate the function directly? f ' (x) = |1| + | 2x - 2| 0 = 2x - 1 x = 1/2 and x from domain = { 0, 2 } the range we get : f(0) = 1 f(2) = 1 f(1/2) = 1/2 + 3/4 = 5/4 min = 1 max...
  44. Buckethead

    B Faraday's disk and "absolute" magnetic fields

    I've posted this here because I think it might be related to the absoluteness of acceleration and rotation. I've been educating myself on the Faraday Disk and was very surprised by one aspect of it. If we have a solid metal disk mounted on a shaft with two electrical brushes contacting the...
  45. Quantum Velocity

    I How can an atom reach less than absolute zero?

    I read a page about making atom under absolute zero. https://www.livescience.com/25959-atoms-colder-than-absolute-zero.html I don't understand very much, if you know pleas help me. Thanks!
  46. H

    The 2 absolute equation equality? find the max and min of x?

    Homework Statement Homework EquationsThe Attempt at a Solution 2x - 1 >= 0 x >= 1/2 x - 2 >= 0 x >= 2 for x <1/2 then 2x - 1 and x - 2 are negative solve : -(2x-1) - (x-2) = 2 -3x + 3 = 2 x = 1/3 for 1/2 <= x < 2 the (2x - 1) positive, (x-2) negative solve : 2x -1 -x + 2 = 2 x = 1 for...
  47. i_hate_math

    Second law of thermodynamics and absolute zero

    Does a system with zero entropy represent the thermal equilibrium at some temperature = 0K? Does the second law of thermodynamics entail that the system will eventually evolve to higher entropy? e.g. a system of 7 magnetic dipoles of paramagnetic spin-1/2 particles in an external magnetic...
  48. M

    MHB Absolute Value Statements....2

    Rewrite each statement using absolute values. 1. The number y is less than one unit from the number t. y < | t - 1 | 2. The sum of the distances of a and b from the origin is greater than or equal to the distance of a + b from the origin. | a + b - 0 | > or = | a + b - 0 | Is this correct...
  49. M

    MHB Is this the correct way to rewrite absolute value statements?

    Rewrite each statement using absolute values. 1. The distance between x and 4 is at least 8. | x - 4 | > or = 8 Can this also be expressed as | 4 - x | > or = 8? If so, why? 2. The distance between x^3 and -1 is at most 0.001. | x^3 -(-1) | < or = 0.001 Can this also be expressed as | - 1...
  50. M

    MHB How to Rewrite Absolute Value Expressions Without Absolute Values?

    The | x | = x when x > or = 0. The | x | = - x when x < 0. Rewrite the following expression in a form that does not contain absolute value. | x + 3 | + 4 | x + 3 |, where x < -3 -(x + 3) + 4 -(x + 3) -x - 3 + 4 - x - 3 -2x - 6 + 4 -2x - 2 Correct?
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