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. tellmesomething

    Electrostatics and current problem with 3 metallic balls

    Theres a picture of the circuit attached. I did not understand how to start the problem since we dont know the distance between the terminal A and the sphere to write the absolute potential at terminal A. So I looked at the solution and im afraid I dont understand it at all. The teacher took...
  2. Agent Smith

    B Relative And Absolute Probability (Probability Of Picking A Red Ball)

    A bag contains ##4## red balls, ##3## green balls and ##2## blue balls. A random ball is selected from this bag. P(ball is red) = ##P(R) = \frac{4}{9}## P(ball is green) = ##P(G) = \frac{3}{9}## P(ball is blue) = ##P(B) = \frac{2}{9}## P(ball is not red) = ##P(\neg R) = \frac{3}{9} +...
  3. M

    Differentiating polynomial absolute value function

    For this problem, The solution is, My solution is, Where I solved these equations to find where the function is ##f(x) > 0## and ##f(x) < 0##. Using ##x^2(1 - x) \geq 0## and ##x^2(1 - x) < 0## First equation: ##x^2 \geq 0 \implies x \geq 0## and ## 1 \geq x## Second equation: ##x^2(1...
  4. Shauryafrom2006

    B I need help understanding the derivation of this 'Absolute Scale of Temperature'

    It is from [ Class 11th] SL Arora, pg no. 11.3, the heading is [11.7] Absolute Scale of Temperature.
  5. ZX.Liang

    I What is “absolute circular polarization fraction” for a pulsar?

    In a pulsar paper, two terms were mentioned: circular polarization fraction and absolute circular polarization fraction. 1. What is the absolute circular polarization fraction? 2. What is the difference between them?
  6. F

    I 3 clocks thought experiment - Absolute vs. relative aspects?

    Here are two similar, quite simple thought experiments, followed by assumptions on final clock readings. In the end, my most important question to them. Exp1: - we have two space ships, ss1 and ss2, both have clocks on board, named cl1 and cl2 - we have a third clock, cl3, somewhere located in...
  7. M

    Why must we use absolute temperature for the Ideal Gas Law?

    For this problem, The solution is, However, why must we use absolute temperature for the ideal gas law (i.e why can we not use Celsius for T) Many thanks!
  8. M

    Trying to understand the property of absolute value inequality

    First lets focus on ##|x|## which is defined as distance between ##x##and ##0##. But if we look into it closely $$13=|-11-2|$$ which is distance between -11 and 2 but $$13=|11-(-2)|$$ which means this is distance between 11 and -2. Which is it? In the same way $$x=|x-0|$$ is distance between 0...
  9. M

    Finding Absolute Uncertainty in Data

    For this data, I am trying to find the overall absolute uncertainty of NA, where NA is the numerical aperture: ##\tan \theta_{NA} = \frac{R}{L}## and ##NA = \sin \theta_{NA}## Case R(cm) L(cm) R/L theta_NA[rad] NA error in NA R0,L0 0.5 0.5 1 0.785398163 0.707106781 0 Rmax,Lmax 0.7...
  10. Euge

    POTW A Test for Absolute Convergence of a Series

    Let ##\{a_n\}_{n = 1}^\infty## be a sequence of real numbers such that for some real number ##p > 1##, ##\frac{a_n}{a_{n+1}} = 1 + \frac{p}{n} + b_n## where ##\sum b_n## converges absolutely. Show that ##\sum a_n## also converges absolutely.
  11. Dario56

    Concept of Absolute Thermodynamic Activity

    In the textbook Electrochemical Systems by Newman and Alyea, Chapter 14: The definition of some thermodynamic functions, chemical potential of component (ionic or neutral) is written as a function of absolute activity: $$\mu_i=RT\ln(\lambda_i)\tag1$$ where ##\lambda_i## is the absolute activity...
  12. M

    I Absolute value bars in dot product derivation

    Dose someone please know why they have the absolute value bars in this derivation? many thanks!
  13. Vectronix

    B Electrons at Absolute Zero -- do they still move?

    Can we all agree that electrons still move at absolute zero?
  14. Leo Liu

    Using Arduino to Obtain Absolute Orientation from a 6-Axis Gyro

    The gyro has 6 inertial axes and 3 magnetic axes. How do I make them work together to get the orientation of the rocket in the reference fixed to the ground? I found something from Matlab but I am not sure how it works...
  15. S

    Solving an absolute value quadratic inequality

    Im a having trouble understanding how this exactly works. $$ |x^2 - 4| < |x^2+2| $$ So I know the usual thing to do when you have absolute values,here it is even simpler since the right part of the inequality is always positive so I just have these 2 cases. 1. ## x^2-4 >= 0 ## and 2. ## x^2-4...
  16. haha0p1

    Finding percentage and absolute uncertainties

    the answers to other parts of the question: a, 2.0×10-⁷ b, 40 N c, O.O5 d, 4×10⁹Pa I Really don't understand how to solve the e part I Know that Young modulus= (Force÷Area)÷(Extension÷Load) kindly guide how to solve this question.
  17. J

    B Rotation is absolute, linear motion is relative?

    Can you explain with example what mean rotation is absolute and linear motion is relative?
  18. C

    Quadratic inequalities with absolute values

    I was given a problem to solve that goes like this ##\frac{3}{|x+3|-1}\geq |x+2|## . I got the correct solution for all possible cases and here they are; for ##|x+3|\geq0## and ##|x+2|\geq## i got ##x\epsilon <-2, -2\sqrt{3} ]## and for ##|x+3|\leq0## , ##|x+2|\leq0## I got ##x\epsilon [-5...
  19. brotherbobby

    Solving an inequality involving absolute values

    Problem Statement : I copy and paste the problem as it appeared in the text to the right. Attempt (mine) : I copy and paste my attempt using Autodesk Sketchbook##^{\circledR}## below. I hope the writing is legible. My answer : I have three answers and confused as to which of them hold...
  20. brotherbobby

    Solving an equality with absolute values

    Problem statement : Let me copy and paste the problem to the right as it appears in the text. Solution attempt (mine) : There are mainly three cases to consider. (1) ##\boldsymbol{x\ge 3\; :}## Using the relevant equations given above, the problem statement reduces to $$x-3+x-2 = 1\Rightarrow...
  21. mcastillo356

    Pattern of variables with absolute value exponents

    On ##x\in{(-1,1)}##, ##x\in{\mathbb{R}}##, ##\forall{n\in{\mathbb{N}}}##, ##x^{|2n|}=O(x^{|2n+1|})## Sugestions? Any answer is wellcome! Greetings, PF
  22. S Holtom

    B Does the CMB give us absolute space and time in practice?

    Another noob relativity / cosmology question (although at least this time won't turn out to be a coding bug, as no code is involved...) AIUI, according to relativity, there is no privileged reference frame, and any inertial reference frame is as "correct" as any other. But... In practice, in...
  23. T

    B Notation for a "scalar absolute field"?

    The notation I think best describes it is ## F = \lVert\int^{space}_s|\vec{V}|ds\rVert ## So you have a vector field V in a 3d space. For each point you integrate over all of space (similar to a gravitational or electromagnetic field) *but* vectors in opposite directions do not cancel, they...
  24. B

    Need help in manipulating rational absolute value inequalities

    How does one manipulate rational absolute inequalities? For example, I want to transform the absolute value inequality ##|x-3|<1## to ##\frac{|x+3|}{5x^2}<A \ ##, for some number ##\text{A}##, to find an upper and lower bound on the latter term using the constraint in the first term, and not...
  25. A

    I How did Charles obtain his law when absolute temperature wasn't define

    Hi all These days I am refreshing my knowledge on the concept and measurement of temperature. One way of defining temperature is in terms of how it is measured. This can be done by observing the variation of some properties which vary linearly with the hotness(temperature) of bodies. I studied...
  26. J

    I Absolute difference between increasing sum of squares

    Given are non-negative integer variables ##x##, ##y## and ##z##. I am trying to deduce the absolute difference between a certain value of ##C=x^2+y^2+z^2## and the very next smallest increase in ##C## possible. I'd like to do this so I can (dis)prove the following: Whether small absolute...
  27. S

    I Because of length contraction, does absolute position exist?

    I know that I have heard that GR proves that there is no absolute time, so does this go for location too? If so, could it be said that particles have a superposition in position/location the same way that particles do in QM?
  28. only1god

    I Is movement really relative or absolute?

    I was discussing in another page this topic with someone. He said it's relative in everything, meaning that energy and force doesn't count. This is obviously wrong because the fact that today we can't (maybe tomorrow we can) know which thing is moving towards the other and which not, doesn't...
  29. patric44

    Problem in evaluating the absolute error

    hi guys i came across this simple question about evaluating the absolute error, the solution is very simple as following : $$ m_{man} = M_{b+m}\pm\Delta\;M_{b+m}-M_{b}\pm\Delta\;M_{b} $$ so the mass of the man alone is $$ m_{man} = (M_{b+m}-M_{b})\pm(\Delta\;M_{b+m}+\Delta\;M_{b}) $$ which would...
  30. wnvl2

    I Absolute meaning of spatial deviaton angle of light around the sun

    Einstein first calculated the bending of light rays that are touching the sun as 1.75 arc-sec. For the calculation I refer e.g. to https://www.mathpages.com/rr/s8-09/8-09.htm I know that spatial angles in general relativity don’t have an intrinsic value (are not invariant). They are dependent...
  31. P

    Engineering Designing an Integrator Circuit with Given Absolute Gain

    For the integrator circuit, I can design the cutoff frequency and the 0dB frequency as required. Using Laplace transforms, the gain is around ##-\frac{1}{sR1C}##, where s is the complex impedance parameter. But, how do I maintain the absolute value of this gain at 10 for the whole band pass for...
  32. J

    I Magnetic dipole in vacuum near absolute zero

    Consider a single atom (or particle) in a vacuum (without electric, magnetic or gravitational field) at near zero kelvin (i.e., no photons or particles striking it). I am curious if it will still have a magnetic dipole? If there still is (which I believe), had this been shown experimentally?
  33. Dario56

    Definition of Absolute Electrode Potential

    Hey guys, I have two questions: 1) I thought absolute electrode potential is galvani potential difference at the interface. However, it is given by this equation in John Bockris - Modern Electrochemistry: $$ E(abs) = ^M\Delta^S\phi - \mu_e^M/F $$ First term is galvani potential difference on...
  34. Shafia Zahin

    I Absolute and relative motion/rest

    In matter of absolute rest and relative rest as per Newton's laws, one thing that confuses me. If a train or bus is moving for example, if one sets aside for a moment the rotation of the Earth and its orbit around the sun, one could say that the Earth was at rest and that a train on it was...
  35. N

    Rewrite an Expression to Eliminate Absolute Value

    See attachment. I don't understand the solution given by David Cohen. 1. Note: x^2 is nonnegative for any real number x. This is because any value for x when squared is positive. Yes? 2. If x is greater than or equal to 0, then I can say that -2 - x^2 is negative in value, right? 3. What...
  36. N

    Simplify An Expression Containing Absolute Values

    See attachment. I don't understand the solution given by David Cohen. I am sure this is a shortcut explanation. I don't like shortcut explanations. 1. What in the problem indicates that x > 1? 2. What in the problem indicates that x < 2?
  37. N

    Absolute Value (algebraic version)....2

    Absolute Value (algebraic version) Rule: | x | = x when x ≥ 0 | x | = -x when x > 0 Rewrite each expression without using absolute value notation. Question 1 | x^4 + 1 | I say x^4 + 1 is a positive value. My answer is x^4 + 1. Question 2 |-sqrt{3} - sqrt{5} | The value of -sqrt{3} -...
  38. N

    Absolute Value (algebraic version)....1

    Absolute Value (algebraic version) Rule: | x | = x when x ≥ 0 | x | = -x when x > 0 Rewrite each expression without using absolute value notation. Question 1 |1 - sqrt{2} | + 1 The value 1 - sqrt{2} = a negative value. So, -(1 - sqrt{2}) = - 1 + sqrt{2}. When I put it all together, I get...
  39. P

    I C in a Vacuum: Evidence of Constant?

    I understand that it is one of Einstein's postulates, however I don't know of any direct experiments which show that it is true.
  40. paradisePhysicist

    Who Can Solve the Mystery of the True Torque?

    Alright how do I explain this. I am looking for the true and absolute equation of torque, specifically, the ratio of angular acceleration to torque. Basically, I got the equations from online, but then found out from another website that most online equations are bogus, my estimate is 99%. The...
  41. R

    Classical Looking for the absolute best fluid mechanics book available

    Dear physics forum dwellers, Currently on search for an advanced fluid mechanics book that covers all the nitty gritty details. Not looking for general introduction books like Munson, Rothmayer, ... or Cengel that are used in bachelor physics classes or engineering classes. Even after skimming...
  42. A

    Finding Absolute Minima & Maxima of a Function

    Good day, I have a question regrading how to find the absolute minima maxima of a function , I understand that first we need to calculate the Hessian Matrix to find the relative minima /maxim but after we need to check the borders of the region ( a rectangle in our case) for example we put x=-2...
  43. Michael c17

    Need help with Finding absolute magnitude

    P is = to 7 and I don't know how to get the absolute magnitude please help.
  44. F

    Whether a non-inertial frame is absolute

    If a frame is a non inertial frame, then it must have an acceleration. Then which reference frame is this acceleration with respect to? If this acceleration varies with the reference frame this acceleration is calculated with respect to, is this non inertial frame absolute?
  45. G

    Absolute zeros other than temperature (e.g. pressure)

    Hi. A version of the third law of thermodynamics states that no system can be cooled down to absolute zero temperature in finitely many steps. But what about other quantities, for example pressure: Is it possible (in principle) to evacuate a system up to the last gas particle, or would this...
  46. cianfa72

    I Is acceleration absolute or relative - follow up

    Hello, Some doubt arose me reading this thread https://www.physicsforums.com/threads/is-acceleration-absolute-or-relative-revisited.999420/post-6454462 currently closed. Sorry, I have not be able to quote directly from it :frown: Your claim is not , however, asserting that the spacetime...
  47. H

    How to Calculate Absolute Gamma Probability from Relative Intensities?

    Hi All, I want to ask how to calculate the absolute gamma probability from relative intensities ( found on the tables of nucliedes) following alpha or beta decay. I mean the probabilities that all add to 1. Many thanks.
  48. Hacker Jack

    Is there such thing as an absolute measurement?

    To want to know the exact quantity of an object whether it be it's length, width, weight etc... Doesn't an absolute measurement only exist in the math/our human Minds. Then go down to quantum scales and that gets even harder because from what point do we even measure from if there is no exact...
  49. A

    B Does Absolute Value Affect Fraction Equality?

    Is it correct that ##\frac{|x + 1|}{|x + 2|}## equal to ##\left|\frac{x + 1}{x + 2} \right|##? Please explain, I don't understand. Thank you
  50. K

    How to represent this absolute value inequality with constants?

    see attached image, it asks to repesent it in x-graph constant "a" isn't conditioned. Do I need to separate it into a few cases of the constant a and represent each in one x-graph?
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