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. 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.
  2. 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...
  3. 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##?
  4. 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?
  5. 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...
  6. 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...
  7. 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...
  8. 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...
  9. 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 -...
  10. 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
  11. 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)...
  12. 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}## ?
  13. 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?
  14. 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 $-7 \le y \le 1$
  15. 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}...
  16. 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 $\frac{1-\ln\left(x\right)}{x^{2}}=0$ $x=e$
  17. D

    Double integral domain with absolute value

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  18. R

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

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  19. R

    B What is Absolute Time and Space?

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  20. 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...
  21. C

    B Neutron Decay Outside of a Nucleus Near Absolute Zero

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  22. T

    Difference between Absolute and Gauge Pressure

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  23. karush

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  24. K

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  25. Thytanium

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  26. Hiero

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  27. GuillemVS

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  28. NP04

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

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  29. 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?
  30. Alfredo Tifi

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

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  31. 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...
  32. SamRoss

    I Necessity of absolute value in Cauchy Schwarz inequality

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

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

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  34. DeusExMachina

    Stargazing Our absolute speed in the cosmos

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  35. 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) =...
  36. A

    Absolute Zero v. The Speed of Light

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  37. G

    Request about experiments on the linear-motion Faraday paradox

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  38. 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...
  39. 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...
  40. R

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

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  41. 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...
  42. K

    Absolute convergence of series

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  43. Wi_N

    Finding Global Max and Min values of an Absolute Function

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  44. 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?
  45. M

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

    Solve the absolute value equation. |(2x + 1)|/|(3x + 4)| = 1
  46. 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.
  47. Mr Davis 97

    I Simplifying this absolute value

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  48. W

    I Proof of a Lemma regarding absolute values

    Hi all, There's this proof that I've been trying to wrap my head around but it just doesn't seem to sink in. I've attached a screenshot below. Many thanks in advance! Consider Case 1. There is a step that goes $$\text{Then} \ |r| = r$$ $$Then -|r| \leq |r| \ \text{and} \ r \leq |r|$$ Why is...
  49. K

    Derivation, absolute value problem

    Homework Statement Find k so that y - 36x = k is a normal to the curve y = 1 / abs(x-2). Homework EquationsThe Attempt at a Solution My problem is regarding the absolute value. I know that the tangent to the curve must be (-1/36). In the solutions manual, it is said that by knowing the sign...
  50. M

    Absolute value equality solution

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