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. anemone

    MHB Absolute value of real numbers

    Reals $x,\,y$ and $z$ satisfies $3x+2y+z=1$. For relatively prime positive integers $p$ and $q$, let the maximum of $\dfrac{1}{1+|x|}+\dfrac{1}{1+|y|}+\dfrac{1}{1+|z|}$ be $\dfrac{q}{p}$. Find $p+q$.
  2. P

    I Is acceleration absolute or relative - revisited

    Hello all, I just joined this group after stumbling over a post from 2003 on this topic. The issue I'd like to deal with is the spinning bucket of water and why the water will still climb up the sides of the bucket if the bucket is stationary. In the original post an Absolutist put it like...
  3. E

    B Volume of a solid at absolute zero

    How much does a typical solid shrink when cooled from room temperature to absolute zero. I can't solve this myself because the coefficient of linear thermal expansion varies with temperature
  4. Kairos

    B Twin Paradox: Radioactive Decay Tested

    If two identical radioactive masses were subjected to the "twin paradox" experiment of Langevin, would the mass that traveled be really less radioactive than the one that did not? Radioactive decay is supposed to be independent of physical conditions and to only depend on the isotope.
  5. Eclair_de_XII

    Python Converting import statements to absolute in PyCharm

    I sort of messed up while writing all my code, and now I regret it. Is there any way to fix all my import statements without manually going through every single one of the modules I created and appending the folder names to the start of each and every imported module name? I am unable to find...
  6. A

    B Properties of Absolute Value with Two Abs Values

    Is it true that ##\frac{|a|}{|b|} = |\frac{a}{b}|## and ##|a| < |b| = a^2 < b^2##?
  7. A

    Is Abstraction an absolute property?

    I came across this line in my java textbook-"Abstraction is the absolute property of a class".i want to know what does absolute property exactly mean and why it is considered an absolute property?Also how does it effect(or is useful) when we practically do programming?
  8. shintashi

    B What is the energy required to approach near absolute zero?

    I'm trying to understand if the amount of effort/energy required to get to absolute zero approaches infinity, or if its a linear thing... is there a point in which dropping near 0 kelvin changes from a 1:1 to an exponential curve? Is the whole thing a curve or is there a static point, like 1...
  9. agnimusayoti

    Fourier series for trigonometric absolute value function

    First, I try to define the function in the figure above: ##V(t)=100\left[sin(120\{pi}\right]##. Then, I use the fact that absolute value function is an even function, so only Fourier series only contain cosine terms. In other words, ##b_n = 0## Next, I want to determine Fourier coefficient...
  10. karush

    MHB -gre.al.9 absolute value domain

    Solve for y: $\quad |y+3|\le 4$ a.$\quad y \le 1$ b.$\quad y\ge 7$ c.$\quad -7\le y\le1$ d. $\quad -1\le y\le7$ e. $\quad -7\ge y \ge 1$ Ok I think this could be solved by observation but is risky to do so...
  11. agnimusayoti

    Absolute value of trigonometric functions of a complex number

    So far I've got the real part and imaginary part of this complex number. Assume: ##z=\sin (x+iy)##, then 1. Real part: ##\sin x \cosh y## 2. Imaginary part: ##\cos x \sinh y## If I use the absolute value formula, I got ##|z|=\sqrt{\sin^2 {x}.\cosh^2 {y}+\cos^2 {x}.\sinh^2 {y} }## How to...
  12. A

    How Do You Solve Complex Absolute Value Inequalities?

    How to solve these two absolute value problems? 1. ##|3x - 5| > |x + 2|## My attempt: From what I read in my textbook, the closest properties of absolute value is the one that uses "equal" sign ##|3x - 5| = |x + 2|## ##3x - 5 = x + 2## ##3x -x = 5 + 2## ##2x = 7## ##x = \frac{7}{2}## ##|3x -...
  13. B

    Speed of sound related to absolute temperature

    Here is the Q Very unsure about how to approach this question but this is what I have tried Any help would be really appreciated! Thanks
  14. jk22

    I CHSH inequality : renaming and absolute values

    In some derivations of the CHSH inequality, https://en.m.wikipedia.org/wiki/CHSH_inequality, the following arises : $$CHS=\int A(a,l1)B(b,l1)dl1-\int A(a,l2)B(b',l2)dl2+\int A(a',l3)B(b,l3)dl3+\int A(a',l4)B(b',l4)dl4\\ =\int A(a,l)B(b,l)dl1-A(a,l)B(b',l)+A(a',l)B(b,l)+A(a',l)B(b',l)dl$$ 1)...
  15. Alexanddros81

    Vector Mechanics — Double Gear Rolling on a Rack

    Hi! My first question: How does he get the equation ##\frac {x_A} {2πr_1} = -\frac {θ} {2π}## ?
  16. A

    I Why is the speed of light absolute?

    To describe the movement of the planets, Newton assumed that there was such a thing as gravity. But he didn't know what gravity was. To derive the Lorentz transformation, Einstein assumed that the speed of light was absolute (not relative), but is it also known why the speed of light is absolute?
  17. karush

    MHB *gre.al.9 GRE Exam Inequality with modulus or absolute value

    given $|y+3|\le 4$ we don't know if y is plus or negative so $y+3\le 4 \Rightarrow y\le 1$ and $-(y+3)\le 4$ reverse the inequality $ y+3 \ge -4$ then isolate y $y \ge -7$ the interval is $-7 \le y \le 1$
  18. D

    Study the convergence and absolute convergence of the following series

    ## \sum_{n=1}^\infty (-1)^n \frac {log(n)}{e^n}## i take the absolute value and consider just ## \frac {log(n)}{e^n}## i check by computing the limit if the necessary condition for convergence is satisfied ##\lim_{n \rightarrow +\infty} \frac {log(n)}{e^n} =\lim_{n \rightarrow +\infty}...
  19. karush

    MHB What is the Absolute Minimum Value of f(x)?

    Let f be the function defined by $f(x)=\dfrac{\ln x}{x}$ What is the absolute minimum value of f a, 1 b. $\dfrac{1}{e}$ c. 0 d. e e. none ok I assume we take the derivative and then set it to zero $\frac{1-\ln\left(x\right)}{x^{2}}=0$ $x=e$
  20. D

    Double integral domain with absolute value

    D={(x,y)∈ℝ2: 2|y|-2≤|x|≤½|y|+1} I am struggling on finding the domain of such function my attempt : first system \begin{cases} x≥2y-2\\ -x≥2y-2\\ x≥-2y-2\\ -x≥-2y-2 \end{cases} second system \begin{cases} x≤y/2+1\\ x≤-y/2+1\\ -x≤y/2+1\\ -x≤-y/2+1\\ \end{cases} i draw the graph and get the...
  21. R

    B Absolute Time, I know its wrong and all but tell me if I got it right

    please tell me if I'm correctly understanding what Newton was trying to say about time being absolute.did he mean that it doesn't matter whether or not you have a clock(which could be any repetetive phenomena) or how that clock is moving, time exists independently of all observation.(that's how...
  22. R

    B What is Absolute Time and Space?

    In physics, the concept of absolute time and absolute space are hypothetical concepts closely tied to the thought of Newton. Absolute, true and mathematical time of itself, and from its own nature flows equally without regard to anything external. There is another term duration measures...
  23. J

    The range for y if t>=10 is [-4, 0].

    From integration by parts, and using y(10) = 0, I get the equation ##2e^{3t-30} = \frac{|y-2|}{|y+1|}.## Let ##f(t) = 2e^{3t-30}##. Since it's for t>10, f(10) = 2, and we have ##2=\frac{|y-2|}{|y+1|}##. Depending on the sign I choose to use, I get either that y=-4 or y =0. Since ##t: 10...
  24. C

    B Neutron Decay Outside of a Nucleus Near Absolute Zero

    Does neutron decay outside of the nucleus occur faster, slower, or at the same speed when the environment it is in is near absolute zero? Do any external factors affect the speed of a neutron decaying?
  25. T

    Difference between Absolute and Gauge Pressure

    Hello all I was wondering someone could help clear up my understanding about the difference between Absolute and Gauge Pressure. After some reading i have been told that the Absolute Pressure is pressure taken at 0 relative to a vacuum. I am trying to understand what this actually means...
  26. karush

    MHB What is the Absolute Maximum Value of f in the Function f(x) = ln(x)/x?

    $\text{22. Let f be the function defined by $f(x)=\dfrac{\ln x}{x}$ What is the absolute maximum value of f ? }$ $$(A)\, 1\quad (B)\, \dfrac{1}{e} (C)\, 0 \quad (D) -e \quad (E) f\textit{ does not have an absolute maximum value}.$$ I only guessed this by graphing it and it appears to...
  27. K

    I Describing entanglement collapse with absolute time

    Why can't absolute time be used to describe events? Previously I tried to describe entanglement collapse on this forum in terms of absolute time, but I was told more or less this was not valid. I don't understand why. If the proper time that we use is based on the fact that the speed of light...
  28. Thytanium

    I Aristotle's Absolute Space & Time: Explained

    Aristotle's absolute space and time can be represented as ordered pairs (s, t) but not as fibers π(s) = t of time as is the case of Galileo and Newton's space time. That is to say that the space of Galileo and Newton is the projection π(s) = t on the time axis. The time space of Galileo and...
  29. Hiero

    I Does a beginning to time imply absolute speed?

    I’m just imagining spacetime that is spatially infinite but has a beginning in time. Naively, there would be only one (class of) reference frame(s with the same velocity) in which time starts simultaneously everywhere. (This is a naive application of “relativity of simultaneity” from SR.) But...
  30. GuillemVS

    How to get the absolute position of a relative object?

    I don't know if this question suits this forum, I post this here actually because I saw (if not my memory is failing) that here it is also possible to solve math problems. So, back on track: I like to discover things from myself, so I searched for the Euler's formula, willing to find the...
  31. NP04

    What is Absolute Pressure and How is it Related to Gauge Pressure in a Pool?

    I think I can eliminate A because the equations depict a linear relationship. Since the gauge pressure is in a linear relationship with the absolute pressure, I would say exactly 2, but the answer is d.
  32. L

    Absolute equation to find the max and min point

    X-1 > 0 x>1 $x^2$ - 2x >0 X>2 For 0<x<1 f(x) = -x +1 + -$x^2 $ +2x For 1<x<2 f(x) = x -1 - $x^2 $ + 2x Find each of the equation the critical point By using f'(x) = 0 And decide which is max and min I get x = 1/2 and x = 3/2 But it's wrong Why?
  33. Alfredo Tifi

    B Is Mach's Principle the Key to Understanding Rotatory Motion?

    I refer to the second paragraph of 1916's book, "Die Grundlage der allgemeinen Relativitätstheorie", translated here. First issue There are two distant stellar bodies, with unchanging shapes: S₁ (spherical) and S₂ (ellipsoidal), made of the same amount and kind of matter. Their centres of mass...
  34. Math Amateur

    MHB Absolute and Conditional Convergence .... Sohrab Proposition 2.3.22 ....

    I am reading Houshang H. Sohrab's book: "Basic Real Analysis" (Second Edition). I am focused on Chapter 2: Sequences and Series of Real Numbers ... ... I need help with the proof of Proposition 2.3.22 ... Proposition 2.3.12 reads as follows: Can someone please demonstrate (formally and...
  35. SamRoss

    I Necessity of absolute value in Cauchy Schwarz inequality

    Reading The Theoretical Minimum by Susskind and Friedman. They state the following... $$\left|X\right|=\sqrt {\langle X|X \rangle}\\ \left|Y\right|=\sqrt {\langle Y|Y \rangle}\\ \left|X+Y\right|=\sqrt {\left({\left<X\right|+\left<Y\right|}\right)\left({\left|X\right>+\left|Y\right>}\right)}$$...
  36. S

    Proving |a|=|-a|: Using Cases and Triangle Inequality"

    Problem Statement: Prove that |a|=|-a| Relevant Equations: ##|a|= a, ## if ## a \geq 0 ## and -a, if ## a \leq 0 ## Somewhat stumped on where to start... i know that we need to use cases. If we consider ##a\geq 0##, then are we allowed to use the fact that ##|-a|=|-1|\cdot|a| = |a| ##? This...
  37. DeusExMachina

    Stargazing Our absolute speed in the cosmos

    Hey everyone, I've watched some youtube videos on special and general relativity. A sentence that I heard over and over again puzzles me. "If I were in a closed space, there would be no way of distinguishing between acceleration and gravity." And there is supposed to be no way of telling how...
  38. T

    How do I determine the uncertainty value of the star's absolute magnitude?

    Homework Statement I have a star that has an apparent magnitude of 13.73 with uncertainty of 0.03303 It's distance Modulus is 13.9967 so it's absolute magnitude is -0.26 The distance is 6300 parsecsHomework Equations [/B] The uncertainty on log10(d) is given by Δ(log10)≈0.4343 Δd/d ΔQ) =...
  39. A

    Absolute Zero v. The Speed of Light

    Hello, I have a physics question that I am hoping the forum can answer. I have lots of them actually, but I would like to start with the one question and go from there. Ideally the answer to the question should be based upon current accepted physics theory. The Question: How do objects...
  40. G

    Request about experiments on the linear-motion Faraday paradox

    The Faraday paradox is a very curious example in the topic of relative motion. An experiment demonstrating the curious results is shown in the video below: This has made me curious about the linear version of the Faraday paradox. A conductor placed atop a magnet, both at rest in one scenario...
  41. F

    How effective is Charles' Law in determining absolute zero?

    Homework Statement Okie so I'm working on my physics work, and I need to compare Charles' Law (for finding absolute zero) to another method used to calculate absolute zero. 3. Attempt at the Solution For this, I was thinking of looking at Carnot engine, but I absolutely do not understand and...
  42. J

    I Relativity & Absolute Position: Exploring the Mysteries

    I am guessing this is an easy one to grasp, but I think I am missing something in my understanding of relativity. Relativity suggests that as an object moves toward the speed of light, a greater amount of force is required to increase its velocity. For this to be true, wouldn't it require the...
  43. R

    B Does time dilation prove the existence of an absolute zero velocity?

    You may think you've seen this before, since I've seen similar discussions in the archives of this, but I think I've distilled the thoughts down to a couple of facts that contradict the common beliefs regarding relativity. Let me preface this with a basic observation: Lorenz invariance does not...
  44. Hiero

    I Change of variables; why do we take the absolute value?

    In transforming an integral to new coordinates, we multiply the “volume” element by the absolute value of the Jacobian determinant. But in the one dimensional case (where “change of variables” is just “substitution”) we do not take the absolute value of the derivative, we just take the...
  45. K

    Absolute convergence of series

    Homework Statement Hello, I need some feedback on whether this reasons is correct. consider the series Examine the series for absolute convergence. Homework EquationsThe Attempt at a Solution How I have solved this, using the limit comparison test: we have: introducing we have that...
  46. Wi_N

    Finding Global Max and Min values of an Absolute Function

    Homework Statement y=0.5x^3 - abs(1-3x), [-2,2] The Attempt at a Solution So i found the min value y(-2)=-11 and i found lokal min at x=sqrt2 There is a sharp max somewhere around x=0.3 but i cannot for the life of me find how to get that point. Also i wrote there is only 1 local min and...
  47. M

    MHB Absolute Value Equation |3x - 2|/|2x - 3| = 2

    Solve the absolute value equation. |3x - 2|/|2x - 3| = 2 Solution: |3x - 2| = 2|2x - 3| 3x - 2 = 2(2x - 3) 3x - 2 = 4x - 6 Solving for x, I get x = 4. However, the textbook has two answers for this problem. The answer is also 8/7. How do I find 8/7?
  48. M

    MHB Solve Absolute Value Equation |(2x + 1)|/|(3x + 4)| = 1

    Solve the absolute value equation. |(2x + 1)|/|(3x + 4)| = 1
  49. M

    MHB Solve Absolute Value Equation |x^2 - 2x| = |x^2 + 6x|

    Solve the absolute value equation. |x^2 - 2x| = |x^2 + 6x| Seeking the first step.
  50. Mr Davis 97

    I Simplifying this absolute value

    I have the expression ##|nr^n|^{1/n}##. A quick question is whether I can allow the exponent to go inside of the absolute value. I know that if it were an positive integral exponent then because of the multiplicativity of the absolute value function that would be allowed. But I'm not sure what...
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