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. V

    Absolute zero and non particle movement

    i have read in some articles that when 0 Kelvin is achieved then particle movement within the cooled substance ceases. but my doubt is that einstein said that all objects have constant movement. this means that if the particles really stop then they will kind of stop in time because it is longer...
  2. W

    Sketching Absolute value graphs

    Homework Statement I previously left some absolute value questions which contained a few simple equations and equalities. i have a further question when it comes to slightly more complicated Absolute statements. Sketch the graph of y = 2|x-1| - 3|x+1| + 3x + 1 Homework Equations...
  3. B

    Inequality with absolute value of a complex integral

    I'm stuck trying to prove a step inside a lemma from Serre; given is 0<a<b 0<x To prove: |\int_{a}^{b}e^{-tx}e^{-tiy}dt|\leq\int_{a}^{b}e^{-tx}dt I've tried using Cauchy-Schwartz for integrals, but this step is too big (using Mathematica, it lead to a contradiction); something...
  4. V

    Absolute value of complex numbers

    When is it true that is |a|=|b|, then either a=b or a=b*, where a and b are complex numbers and b* is the complex conjugate of b?
  5. kandelabr

    Volume work, absolute and relative pressure confusion

    hello. i can't figure out where I'm wrong. this is the problem: we have a cylinder, closed with a piston. the absolute pressure inside the cylinder is p0, atmospheric pressure is patm. the air inside expands isothermally to some (specific) volume vend. i derived the equation for...
  6. B

    Cauchy Integral with absolute value in simple curve

    Homework Statement Integrate using Cauchy Formula or Cauchy Theorem: I=\oint_{|z+1|=2}\frac{z^2}{4-z^2} dz (From Complex Variables, Stephen Fisher (2nd Edition), Exercise 2.3.3) Homework Equations \frac{1}{2\pi i}\oint_{\gamma} \frac{f(s)}{s-z} ds= \left\{ \begin{array}{lr}f(z) & : z \in...
  7. K

    Absolute voltage values at battery terminals

    Hi all, Lets say i have a battery with a rated voltage of 3V. This means that there is a potential difference of 3 V across the +ve and -ve ends of the battery. This can mean 3V/0V, 5V/2V, 6V/3V and the list of possible combinations goes on. My question: Is there any way of knowing the...
  8. D

    Calculating absolute magnitude and apparent magnitude

    Ummm... never mind, we found it... Homework Statement Given Proxima Centauri with parallax angle of 0.769" and apparent bolometric magnitude of 11.1... what is its absolute magnitude?Homework Equations I get that I should use m-M = 5 log10(d/10 pc) and I understand that d = 1/p". What I...
  9. V

    Reaching absolute zero and BEC

    Why are we finding it so difficult to reach absolute zero and if at all we are able to achieve it then what are the implications of such a feat? What relation does a bose einstein condensate have with absolute zero? (i know that we have achieved it but how does it happen as we lower temperatures)
  10. D

    What is the limit of |x+1| as x approaches -1?

    Homework Statement Evaluate. lim |x+1| x-> -1 Homework Equations The Attempt at a Solution Not too sure what |x+1| means. I think it has something to do with an absolute value... would the answer be 2 then?
  11. N

    Is the converse of the absolute value limit theorem true?

    Hi all, I'm wondering about this question I can prove that if lim_{n->inf} (a) = L then lim_{n->inf}abs(a) = abs(L) however.. is the converse true? thx
  12. M

    Lorentz force: absolute reference frame?

    F= q(v x B) B= v x q*k*d/r^2 It is a basic physics knowledge magnetic field forms around moving charge, it tell us magnetic field is zero when charge is not moving and strength of magnetic field increases as velocity increases, right? Magnetic potential vector field increases with "absolute...
  13. S

    Dealing with absolute value functions

    In order to get an integral I need to find the difference between two functions, but I'm not sure how to deal with the absolute value... f(x) = \left|x-1-1\right| g(x) = x^2 + 2x g(x) - f(x) = (\left|x-1\right|-1) - (x^2 + 2x) =... I don't know if I can simplify it anymore... can I...
  14. D

    Exploring a function f(x) with absolute value

    when i am exploring a function eg. f(x)=|2x-6| can i treat it as two separate function all the way through, one to the left of x=3 and one to the right, and only at the very end, when i draw the graph connect them, ie draw a graph according to all the values i found from each side? will this...
  15. P

    How Do Absolute Values Affect Solving Function Equations?

    Homework Statement I do not see how the two equations in each example are related, what should I do with them? (the l's are absolute value brackets): a) Let g(x) = 3x - 3 + l x+5 l. Find all values of a which satisfy the equation: g(a) = 2a +8 b) Let h(x) = l x l - 3x...
  16. T

    Confused about the absolute value of a complex number

    Let z be the complex number: x+iy. Then |z|^2=x^2+y^2 according to my book. But according to the general definition of absolute value, |a|=(a^2)^.5. So letting z=a=x+iy. |z|^2=z^2=x^2+2ixy-y^2 This is not equal to x^2+y^2. I'm confused.
  17. G

    Is there the possibility of absolute time

    Is there the possibility of "absolute time" Is there a theory of absolute time that is compatible with General Relativity? (This question inspired by a thread on http://www.freeratio.org/showthread.php?p=5740883#post5740883".)
  18. S

    What is absolute reference pressure and absolute reference temperature

    What is "absolute reference pressure and absolute reference temperature" I am doinf a test about compressed air flow rate. There is a parameter called absolute reference pressure and absolute reference temperature. Are they 1.01bar and 273+20K?
  19. U

    Calculating integrals of area between two functions, involving absolute values

    Hi all, I'm currently preparing for pre-tertiary mathematics, studying from Apostol's "One-Variable Calculus". I have just begun to work on the theory of integration of trigonometric functions, but I found that with the last set of exercises (on finding area between two functions, over some...
  20. N

    Error Analysis of Experiment Data: Calculating Percentage and Absolute Error

    Homework Statement In my latest experiment, I have found two sets of data from the data processing. Normally, the values in the data sets should be equal, but they are not as a result of the error of the experiment. How can I do the error analysis? (Percentage Error, absolute error...)...
  21. U

    Limit of a function with absolute value of polynomial in a quotient

    Homework Statement Find: Lim | x2+x-12 |-8 / (x-4) x --> 4 Homework Equations The Attempt at a Solution My answer is 9. It it right ? or there is not a limit for F(x) when x --> 4
  22. T

    Is it possible to reach absolute zero?

    So, from what I've heard, absolute zero is 0 Kelvin, lowest temperature possible, -273.15 C, etc etc. Is it possible to even reach it? Why or why not?
  23. D

    Absolute Converge test for 1/[n*ln(n)]

    Homework Statement \sum_{n = 2}^{\infty} \frac{1}{n*ln(n)} I have to find whether the series absolute converge, conditionally converge or diverge?2. The attempt at a solution I used the ratio test. so, lim(n to infinity) [n*ln(n)]/[(n+1)*ln(n+1)] since ln (n+1) will be...
  24. G

    Finding absolute minimum and maximum values

    Homework Statement Find the absolute minimum and maximum values of f on the set D. f(x,y)= e-x2-y2(x2+2y2); D is the disk x2+y2 <= 4 Homework Equations Second Derivatives test, partial derivatives The Attempt at a Solution fx(x,y) = 0 = (e-x2-y2)(-2x) + (x2+2y2)(-2x...
  25. W

    Integral of Absolute Value Function

    Homework Statement \int^{8}_{0}\left|x^{2} - 6x + 3\right|dx This is for a single variable AP Calculus AB class in which we are solving using substitution method. 2. The attempt at a solution I attempted it by just ignoring the abs value bars thinking that anything I am finding out...
  26. A

    Absolute and Conditional Convergence Problem

    Homework Statement Test the series for (a) absolute convergence, and (b) conditional convergence. \sum\left(-1\right)^{k+1}\frac{k^{k}}{k!} Homework Equations The Attempt at a Solution So I tried taking the absolute value and then applying the ratio test, which, after...
  27. D

    Manning's coeff to absolute roughness

    Does anyone have the equation that the absolute roughness is expressed in terms of Manning coefficient, with the reference included? I have found one from Webber 1971. n = k1/6/26 where: n = applicable Manning roughness coefficient, k = absolute roughness (mm) Reference :Webber...
  28. A

    Absolute Entropy in an isolated gas

    Given an ideally isolated volume of a single species of gas that has reached internal equilibrium , would the individual molecules : [A] Retain the range of individual velocities and thermal energies [if present] and keep a merely statistically constant average...
  29. T

    Absolute value of a function integrable?

    this is the question, Prove that if f is continuous on (a,b] and if |f| is bounded on [a,b] then f is integrable on [a,b]. (note: it is not assumed that f is continuous at a.) I know you have to use the upper and lower bounds to prove this statement but i don't know where to start...
  30. T

    Absolute value of a function integrable?

    this is the question, Prove that if f is continuous on (a,b] and if |f| is bounded on [a,b] then f is integrable on [a,b]. (note: it is not assumed that f is continuous at a.) I know you have to use the upper and lower bounds to prove this statement but i don't know where to start? Thanks
  31. L

    Absolute min/max (algebra+solving for zero), Rolle's Thrm

    Hey everyone. Just getting prepped for a midterm on Tuesday and looking for a bit of help on a few things. If there are any tricks to make some of this stuff easier that would be great. I remember there being a few from back in high school, but i can't remember them. I know the process for all...
  32. L

    Absolute symmetrical sphere become unsymmetry

    Say we have an absolute sphere ball which is consist of an fully filled with air which the ball cannot expand anymore, as further pumping air will cause the ball explode. As a few air inside is leaked, the ball will not shrink since its membrane is inelastic, hence causing the ball to become a...
  33. S

    Trying to derive this but has multiple absolute values

    Homework Statement Find the Local and absolute extrema of f(x) on the interval [-1,2] and give a sketch of the graph if: f(x) = [ 1 / (1 + |x|) ] + [ 1 / (1 + |x - 1|) ] I am confused about the absolute value parts. I know they're the versions inside the absolute value signs when...
  34. M

    Does Divergence of a Series Imply Divergence of Its Absolute Values?

    Homework Statement Show that following statement is true: If Σa_n diverges, then Σ|a_n| diverges as well. Homework Equations Comparison Test: If 0 ≤ a_n ≤ b_n for all n ≥ 1, and if Σa_n diverges, then Σb_n diverges as well. The Attempt at a Solution I tried to prove the...
  35. A

    Deriving absolute error equation

    Homework Statement I need to derive an error equation from the following equation... \frac{e}{m} = \frac{2V}{B^{2}R^{2}}Homework Equations Just... basic... derivation rules...The Attempt at a Solution I did try, just don't know how to put the stupid attempt in LaTeX... I'm stuck at the "2V"...
  36. F

    Indefinite Integral of an Absolute Convergent Function

    Hi, I was wondering if a function is absolutely convergent over a certain interval, say, (0,\infty) will its indefinite integral also be absolutely convergent over the same interval? Also, assume that f(x) is convergent for (0,\infty). Would g(x) = \int{\int_{0}^{\infty}f(x)dx}dy &=&...
  37. J

    Absolute Extrema of Trigonometric Functions on Closed Intervals

    Homework Statement Find the absolute max and absolute min values of function on the given interval: f(t) = 2cos(t) + sin(2t), [0,pi/2] Homework Equations The Attempt at a Solution f '(t) = 0 0 = -2sin(t) + 2cos(2t) 2sin(t) = 2cos(2t) stuck...
  38. R

    How to Evaluate the Absolute Value Integration?

    1. Evaluate \int_{-1}^{3} \left|x^2 -4\right| dx 3. The Attempt at a Solution This is the first time I'm trying this type of question & I think I need to use the following theorem for such questions; f is integrable on a closed interval a to b. \int_{a}^{b}f(x)dx =...
  39. Z

    Absolute Minimum and Maximum Word Problem

    Homework Statement Find a number in the closed interval [1/2, 3/2] such that the sum of the number and its reciprocal is (a)as small as possible (b) as large as possible I am given the answer in the back of the book The answer to a is 1 The answer to be is 1/2 Homework...
  40. J

    How was absolute 0 calculated?

    Hi, according to 3rd law of thermodynamics, absolute 0 can never be attained. But i really don't understand how was the exact value of absolute 0 calculated almost 100 years back? I think it comes from the thermodynamic relationships, but i don't understand how. Can anyone explain me the...
  41. R

    Divisor proof with absolute values

    Homework Statement I reduced a much harder problem to the following: Prove that if abs(a-b) is divisible by k, and if abs(b-c) is divisible by k, then abs(a-c) is divisible by k. Homework Equations none really. The Attempt at a Solution I tried setting abs(a-b)/k = n and abs(b-c)/k = m...
  42. M

    Help, need to get down absolute value equations and inequalities.

    I'm taking an algebra & triginometry class at my college and my professor is kind of slow and unclear. I think I'm a fast learner and a good understander which is why I came here to get this info down. We're up to complex fractions or radical equations right now I think, forgot which. Something...
  43. M

    Solving quadratic inequalities and absolute values

    Homework Statement lxl <2 lx+2l The question is asking to solve this Homework Equations The Attempt at a Solution Ive tried bringint the 2 over which leads me to l-x-4l over lx +2l < 0 but then the absolute value confuses the heck out of me on where to go...
  44. G

    Is it possible to reach absolute zero and still be affected by gravity?

    Today in my physics class we got into a discussion about Absolute Zero and gravity. The argument was that if Absolute Zero was achieved, would it still be affected by gravity? Because gravity is a force and would make whatever that was at Absolute Zero move, but to have motion there would be...
  45. T

    Proving Absolute Value Inequality: |a| ≤ b → -b ≤ a ≤ b (b≥0)

    Prove the following: if |a| \leq b then -b \leq a \leq b (where b \geq 0 ). So a \leq b and -a \leq b . Then -b \leq a so that -b \leq a \leq b . Suppose that -b \leq a \leq b . Then a \leq b and -a \leq b so that |a| \leq b . Is this a correct proof? You don't have to...
  46. G

    Expressions without absolute value signs

    Homework Statement Rewrite the following expressions without absolute value signs, treating various cases separately where neccesary Homework Equations a-Abs[(a-(abs)a)] the question is do i have 2 answers to this ?
  47. P

    Is there an absolute maximum value of this function?

    Homework Statement Consider the function f:R^2->R defined by f(x,y)=[e^(x+y)]-y+x. Is there an absolute maximum value of f on the set s={(x,y):/x/+/y/<=2}? Justify. note, /x/ is the absolute value of x. Homework Equations a. If f is con't, it takes compact sets to compact sets...
  48. G

    A natural log inequality with absolute value

    Homework Statement F(x) = (8-12ln|x|)/(x^4) > 0 (a) For what values of x is the expression F(x) defined? Write your answer in interval notation. (b) At what value(s) of x is the expression F(x) equal to zero? If there is more than one answer separate them by commas. (c) The set of...
  49. H

    Calc 1 - derivative of absolute value

    Homework Statement Question is: how can you tell if there are any places you can't take the derivative of an equation that has an absolute value (using logic, not just graphing it) example equations 1. \left|x-5\right| 2. \left| x3+4x2+9x+17 \right| x2+1 3...
  50. N

    Why is the absolute value of x equal to -x for values under zero?

    Here, it says that for the limit f(x) = |x| / x, |x| = { x, x > 0 -x, x < 0 } What I don't undestand is why is |x| = -x for values under zero? Isn't the absolute value for negative values just x and not -x? thanks. EDIT: I don't want to start a new thread, but I got stuck on this...
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