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. S

    Gravitational Force on a Body: Is it Absolute?

    Can we consider gravitational force acting on a body considered as absolute force:-) if so pleas explain
  2. S

    Minimum Absolute Value of a nxn Matrix Determinant

    The following matrix problem occurred to me. I figured out the answer and would like to pose the problem. It's easy but would be best for an undergrad math major. The question: Consider a square n by n matrix with entries 1, 2, ..., n squared. Find a way to arrange these entries so that the...
  3. R

    Help resolving absolute motion paradox please.

    Hi, I’ve been teaching myself SR, currently reading Relativity for the Questioning Mind by Daniel F Styer. My math is not great, so I have been avoiding the heavy calculations for now. I will learn those too, but I wanted to understand the concepts first. For the most part I think I have...
  4. S

    Solving integrals with absolute values

    Homework Statement solve the integral [abs(x+1)(3+abs(x))]/(x+1) between -3 and 1 Homework Equations The Attempt at a Solution when x<-1 then [abs(x+1)(3+abs(x))]/(x+1) = [-(x+1)(3-x)]/(x+1) = -(3-x) when -1<x<0 then [abs(x+1)(3+abs(x))]/(x+1) = (x+1)(3-x)/(x+1) = 3-x when x>0...
  5. S

    Integration with absolute values

    Homework Statement if f(x)=abs(x-2) and g(x)=abs(x), then solve the integral from -1 to 3 of abs(f(x)-g(x))dx Homework Equations The Attempt at a Solution resolved absolute values: when x<0, abs(x-2)-abs(x) = -x-2+x = 2 when 0<x<1, abs(x-2)-abs(x) = (-x+2)-x = 2-2x when 1<x<2...
  6. Z

    CMB and Absolute Rest: Resolving Contradiction

    I'm having trouble resolving the contradiction between theories of the Cosmic Microwave Background, and Special Relativity. Einstein denied the existence of any absolute standard of rest. As einstein-online.info paraphrases: "In the real world, there exists no such state of absolute rest...
  7. 5

    Solving an equation with an absolute value within an absolute value

    Homework Statement Solve the equation | | 3x + 1 | - x | = 2 Homework Equations |x| = x if x \geq 0 |x| = -x if x < 0 The Attempt at a Solution To start, I have never dealt with such an equation before, and am partly 'iffy' with absolute values in general, but, up...
  8. J

    What happens to water at just above absolute zero degrees?

    I know that water forms different kinds of crystals in different kind of temperatures but is there any temperature where water is solid but does not form crystals for example just above absolute zero degrees, what kind of crystals does it form?
  9. 1

    Is ln|sin x| equivalent to ln sin x?

    Homework Statement y = ln | sin x | Homework Equations - The Attempt at a Solution No attempt at a solution, because it's more of a "which part of this is incorrect" question. y = ln | sin x | Would everyone agree that this is equivalent? y = ln \sqrt{(sin x^2)} Then...
  10. W

    Absolute Value Integrals

    Homework Statement ∫ |x^2 -9| [0-4] Homework Equations The book answer states the same EXCEPT splits into [0-3] and [3-4]. Other problems split the integral perfectly in half for absolute values...why would it differ and are there rules to figure this out? Larson's Calculus has no...
  11. R

    Absolute Maximum and Minimum Values over a given interval

    Homework Statement Find the absolute maximum and absolute minimum values of the function (x^3)+(12x^2)-27x+9 on each of the following interval [-10,0] The Attempt at a Solution I got this and its saying its wrong. y'= (3x^2)+(24x)-27 factor: 3(x^2+8x-9) so x=-9 and x=-1 y''=6x+24...
  12. icesalmon

    Absolute or Conditional Convergence, or Divergence of Alternating Series.

    Homework Statement given an = ( -1 )(n+1) / \sqrt{n} determine if the infinite series is Absolutely Convergent, Conditionally Convergent, or Divergent. Homework Equations I hope I have these theorems down correctly, please correct me if I'm wrong. If \Sigma|an| is Convergent then...
  13. N

    Can Particles Retain Information at Absolute Zero?

    can a particle hold it's information at absolute zero?
  14. F

    Interesting Absolute Value problem

    Homework Statement Find all x in |5x-2| = 6x-12 The Attempt at a Solution http://www.wolframalpha.com/input/?i=Plot[|5x-2|+%3D+6x-12%2C{x%2C-1.5%2C1.5}] Notice how only x = 10 is a solution? So my question is, why isn't x = -14/11 a solution? I mean sure they don't...
  15. I

    Finding the absolute value (modulus) and solving equation

    [b]1. | (2-i)(3+2i)(-5-6i)(-7+3i) / (-4+i) | Homework Equations [b]3. I am pretty sure I am not computing it right but this is what i come up with. square root of 5* square root of 13* square root of 61* square root of 58 / square root of 17.
  16. P

    Why is the speed of light absolute?

    Special relativity upended our normal conceptions of space and time by postulating that the speed of light was absolute for all observers. So rather than the absolute space and time of Newton, Einstein postulated an absolute speed of light, which by necessity leads to a malleable space and time...
  17. T

    Proving Absolute Convergence of Gamma and Beta Integrals in Complex Analysis

    Homework Statement Let z,p,q \in \mathbb{C} be complex parameters. Determine that the Gamma and Beta integrals: \displaystyle \Gamma (z) = \int_0^{\infty} t^{z-1} e^{-t}\;dt \displaystyle B(p,q) = \int^1_0 t^{p-1} (1-t)^{q-1}\;dt converge absolutely for \text{Re}(z)>0 and p,q>0...
  18. N

    Precal, Inequalities involving absolute value

    Homework Statement DIRECTIONS: Express the intercal in terms of an inequality involving absolute value. PROBLEM: (-4, 4) MY STEPS: 1: (-4, 4) 2: -4<x<4 3: |x|< 4 MY ANSWER Is that correct? Is step 3 correct? The only reason that I included that part is becuase it says...
  19. F

    Absolute Value with Quadratic: What Are the Solutions to |x^2 + 6x + 16| < 8?

    Homework Statement Very embarrassing that I had problems with this. I managed to solved it at the end, but I am posting this for two reasons 1) I like someone else to work it out in a different method, I wnt to see what other approaches there are 2) Whether mine is taking too long or not. I...
  20. O

    Opening switch on inductor circuit in absolute vacuum

    So, a professor in class a about a year ago mentioned that opening a switch in a circuit that an inductor is providing power to would cause a breakdown in the air and a spark would jump across it because the current can't change instantaneously to zero in an inductor. Something just made me...
  21. A

    Integrating Factor and absolute value

    Hi, I have a general question regarding the integrating factor of first-oder linear DEs. All textbooks that I've seen (which aren't too many) simply drop the absolute symbol when the factor has the form exp(ln(abs(x))). This would evaluate to abs(x), yet the books use simply x. Why is that...
  22. I

    Proving Absolute Value Convergence of Sequence to A

    Homework Statement If the absolute value of a sequence, an converges to absolute value of A, does sequence, an necessarily converge to A? Homework Equations convergence: a sequence { an}n=1-->infinity, converges to A є R (A is called the limit of the sequence) iff for all є > 0, there...
  23. F

    Rotation tensor and absolute time

    Hi to all ! I have been doing some research in Godel's universe (I have just finished my first General Relativity course so I'm not an expert yet) and there is something which is still not clear to me. Can someone explain me why the fact of having a non vanishing angular velocity implies that...
  24. O

    Absolute beginner hobbyist wondering where to start

    So I'm going into a physics major next year, but lately I've been interested in electronics. Not enough to switch majors, but I'd like to take it up as a hobby at least. Unfortunately, I have absolutely no experience. I have the Circuit Analysis book that EE majors at my school use for the very...
  25. M

    Absolute Zero and implications

    I'm not a scientist, but I really enjoy reading the perspectives on these boards. I have some questions I hoping to hear a lot of perspectives on. I know absolute zero has never been reached, but in what ways are we attempting to find absolute zero currently? If, hypothetically, we were...
  26. R

    Simultaneity question – is sequence absolute?

    There are two space stations A and B which are at rest wrt to each other and separated by some distance x. Each space station has a light that randomly flashes. I am in a third space station, somewhere in the middle of A and B and at rest wrt to the other two stations. I see Station A’s...
  27. S

    Particular solution of nonhomog. euler equation Messy absolute values in integral

    Homework Statement Solve the IVP (x^2)y'' + 4xy' - 40y = x^6 for y(1) = 10, y'(1) = 1Homework Equations not so much "equations" but here I try to use variation of parameters to get the particular solution.The Attempt at a Solution FOR THE HOMOGENEOUS SOLUTION: using the substitution y = x^r...
  28. K

    Absolute parallelism in teleparallel gravity

    I am reading Hayashi's paper titled "http://prd.aps.org/abstract/PRD/v19/i12/p3524_1" " (Phys. Rev. D 19, 3524, 1979). In Riemann-Cartan geometry, one can choose the Weitzenbock connection rather than the well-known Levi-Civita connection, so that Riemann curvature tensor vanishes while the...
  29. G

    Absolute value of complex number

    Homework Statement Let R be a set of real numbers derived from rational numbers. And, let R* be a set consisting of all ordered pairs of the form (x,0) where x is an element of R. For a complex number z = (a,b) = a+ib, I've learned that the absolute value of z is the number...
  30. P

    Why is absolute zero important in the PV = nRT formula?

    Hi, Today in school I performed an experiment that went like this: We had a capillary tube with trapped air on the bottom, the top part was open to the atmosphere and, in between, there was some sulphuric acid. We heated the capillary tube and recorded the increase in volume of the trapped...
  31. K

    Are the directions of charge flow (=current?) absolute?

    Let's say I have two (-) charged beams. According to observer 1: Beam 1 is shot at 0.998 c. Beam 2 is shot at 0.999 c. >> Therefore, the beams are moving in the same direction. Observer 2 is moving at 0.9985 c. Observer 3 is moving at 0.9995 c. According to observer 2: Beam 1 is shot at -0.143...
  32. E

    Absolute Equation: Solving for x with 2(2)^0.5 and (5)^0.5

    Homework Statement |2(2)^0.5 -3|+|3+(5)^0.5|=x Homework Equations why is the answer 6-2(2)^0.5 +(5)^0.5 and not 2(2)^0.5 + (5)^0.5 The Attempt at a Solution the answer multiplied - into the first absolute. why arent the other combos the answer?
  33. T

    Absolute value function is the Heaviside step function

    Homework Statement [PLAIN]http://img845.imageshack.us/img845/1706/delta.png The Attempt at a Solution This question has come after a chapter on Dirac's delta-function although the question doesn't say use it. Could I use it? If not how do I do it directly?
  34. ECHOSIDE

    Absolute value appears on both sides of equals sign

    Homework Statement solve for x: 5|7-3x|+2=4|7-3x|-1 Homework Equations The Attempt at a Solution 7-3x>0 -3x>-7 x<3/7 {x|x<3/7} quantity is positive {x|x>3/7} quantity is negative I have never solved an equation with more than one absolute value quantity in it and am not sure how to start...
  35. P

    Can you determine absolute motion?

    I have heard it said that an object not feeling acceleration cannot determine if he is in motion unless he sees another object to compare himself too. But what if you had an apparatus that was made of two spheres. One inside the other. Perfectly centered on each other. The inner sphere emits...
  36. W

    Absolute value inequalities

    Homework Statement I was trying to show that 1) |a+b|≤|a|+|b| 2) |a+b|≥|a|-|b| and find out how they were true when a,b>0, a,b<0, and a>0,b<0 Homework Equations 1) |a+b|≤|a|+|b| 2) |a+b|≥|a|-|b| The Attempt at a Solution For |a+b|≤|a|+|b| a,b>0 I got that |a+b|=a+b...
  37. A

    Absolute Convergence, Conditional Convergence or divergence

    Absolute Convergence, Conditional Convergence or divergence... Homework Statement \sum_{n=1}^{\infty} \frac {(-2)^{n}}{n^{n}} Homework Equations \lim_{n \rightarrow \infty} | \frac {a_{n+1}}{a_n}| < 1 \;\; absolute\; convergence \lim_{n \rightarrow \infty} | \frac...
  38. jfy4

    Absolute convergence, boundedness, and multiplication

    Homework Statement If the series \sum_{n=1}^{\infty}x_n converges absolutely, and the sequence (y_n)_n is bounded, then the series \sum_{n=1}^{\infty}x_ny_n converges.Homework Equations Definitions and theorems relating to series and convergence.The Attempt at a Solution If the sequence y_n is...
  39. V

    Where is it appropriate to place absolute value bars while solving this diffeq

    Homework Statement just a simple problem as an example dy/dx = y/x dy/y = dx/x Homework Equations The Attempt at a Solution dy/y = dx/x ln|y| = ln|x| + c then when I take exponents do I still have to include the absolute value bar |y| = |x|c
  40. R

    A question about Absolute Zero

    This is highly theoertical and I came up with it taking a standerized test. So without further adoo, What would happen if you to a cyrogenic chamber froze something to ablsolute zero and put it on a spacecraft moving at exactly the same velocity as the universe is. Thus canceling out...
  41. Q

    Absolute Zero - No Entropy -Quantum Jiggles?

    When something is frozen fully, and the temperature is absolute zero -there is no entropy - but does that mean the "quantum jitters" are not occurring?
  42. S

    How a Absolute value Function can be continuous?

    Hello friends, I am quite confused how an absolute function is called a continuous one. f(x) = |x| has no limit at x=0 , that is when x > 0 it has a limit +1 {+.1, +.01, +.001} and -1 when x <0 {-.1, -.01, -.001} that is the reason it's not differentiable (left and right side limits are not the...
  43. 4

    Twin Theory and Absolute Zero?

    I was just wondering. With the Twin Theory, with the person traveling at the speed of light causes them to age slower. So I wondered, does that mean that something would age faster if at absolute zero? Because I've heard that motion is relative to temperature, and time is relative to velocity...
  44. J

    Charles' law and absolute zero

    According to Charles' law, volume decreases with temperature. Extrapolating down towards absolute zero, and the volume of the gas will be zero. How can this be possible? Surely any amount of gas will still have to take up some volume in space. Can multiple gas molecules really occupy zero volume?
  45. B

    Could a High Temperature Absolute Encoder Fill a Niche Market?

    Hi, as part of a project I needed a slim (<10mm) small diameter (<30mm) through hole absolute encoder that works at 100 degC. I wanted this to be able to determine a motorized valve position, so it needed to slip onto the gearbox output shaft between the motor and the valve. Anyway, I...
  46. A

    Can someone please confirm or deny this assertion about absolute convergence?

    EDIT: On pg. 390 of Kreyszig's Functional Analysis text, we have: "If T is a bounded linear operator on a nonempty Banach space, then the series \sum_{k=0}^\infty \left( \frac{T}{\lambda} \right)^k converges absolutely for |\lambda| > 2\| T \|." The argument presented in Kreyszig...
  47. G

    Total absolute curvature of a compact surface

    Total "absolute" curvature of a compact surface Hi! Someone could help me resolving the following problem? Let \Sigma \subset \mathbb{R}^3 be a compact surface: show that \int_{\Sigma}{|K|\mathrm{d}\nu} \ge 4\pi where K is the gaussian curvature of \Sigma. The real point is that I want...
  48. S

    Double integrals with an absolute value

    Homework Statement Im getting very confused with working out how to integrate the following double integral with an absolute value: \int^{2}_{-2}\int^{2}_{-2}\left|x^{2}+y^{2}-1\right|dxdy Homework Equations The Attempt at a Solution I know you have to split it down into where it...
  49. russ_watters

    Derivative of Absolute Value Confusion

    Quick question (hopefully): I'm helping my girlfriend with some calculus homework over the phone and it looks like the book has a different answer for the derivative of an absolute value than I'm seeing in other places. I'm seeing it as (and I derived it myself to be) x/abs(x) whereas the book...
  50. G

    Is time dilation relative, or absolute?

    I explain my question through an example. If we brought down a GPS clock, would it show the normal time, because it was accelerated before launch, but it has been slowed down by time dilation? Or we have to accelerate those clocks in order to compensate for the time loss, till the signal from...
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