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. P

    Apparent Birghtness And Absolute Brightness

    Question: Considering the effect of an Earth sized plaent transiting a star, and blocking its light. How big will the change in ABSOLUTE birghtness be for different stellar classs O and A, if we subtract off this blocked light. telescopes can detect very small changes in brightness...
  2. P

    Max/Min of f(x,y): Answer & How-To

    Homework Statement Max/min of f(x, y) = 1/x + 1/y Constraint 1/x^2 + 1/y^2 = 1 The Attempt at a Solution This was a question on my midterm exam and I am just wondering what the right answer would be. With lagrange multipliers, I got two candidate points (sqrt (2), sqrt (2)) and (-(sqrt...
  3. bland

    CMBr & Absolute Motion: A Query

    Why can't the CMBr 'wall' that is as if we were in the middle of a sphere surrounded by it, be used as a reference point for absolute motion in space?
  4. O

    Absolute value inequality

    Question: True or False If x^2<4 then |x|<=2 My solution: I get -2<x<2 when I solve the problem so it should be false. Yet the text says its true? Is this a mistake? If |x| is equal to 2 then it should be a closed interval, not an open interval which seems to be correct to me.
  5. F

    MHB Derivative of function containing absolute value

    I'm working on a ODE with initial conditions y(2)=4 and y'(2)=1/3. I solved it to be y=\frac{c_1}{|x-6|^8} + c_2|x-6|^{\frac{2}{3}}. How do I apply the second initial condition? I'm stuck at taking the derivative.
  6. C

    Finding the absolute minimum of a function in R2

    Homework Statement Use technique of completing squares to Show that this function has an absolute minimum. f(x, y) = x^2 + y^2 − 2x + 4y + 1 Homework Equations Not entirely sure how completing the squares will indicate an absolute minimum.Is there some additional reasoning required? The...
  7. R

    Difference between the absolute thermodynamic temperature scale and ITS-90

    Homework Statement What is the difference between the absolute thermodynamic temperature scale and the practical temperature scale: ITS-90? Homework EquationsThe Attempt at a Solution
  8. B

    Is Absolute Value a Useless Concept?

    Is this mathematical concept EVER used in real life or "higher" levels of math? I just find it to be a practically useless thing. It's like some guys sat around and invented this math concept just for the sake of it. Or, am I wrong?
  9. F

    MHB Why does integral of 1/x have absolute value?

    I lost a mark for integrating \frac{1}{x} to ln(x) instead of ln\left| x \right|. Since the derivative of ln(x) is \frac{1}{x} not \frac{1}{\left| x \right|} why is this the case?
  10. M

    Properties of natural log and absolute value

    Homework Statement from -lnIxI to lnI x^-1I , I try to go from -lnIxI to lnI x^-1I by using some properties. Homework Equations - lnIxI The Attempt at a Solution First I write the -lnIxI as -1*lnIxI and then I use -1 as an exponent to absolute value of x in the natural log that is ln (...
  11. adjacent

    What is the solution to the absolute function problem?

    Homework Statement ##|x^2-2| \leq 1## Find ##x## The Attempt at a Solution ##x^2-2\leq 1## ##x \leq \sqrt{3}## and ##-(x^2-2)\leq 1## ##-x^2+2 \leq 1## ##x \geq 1## Therefore the solution is ##1 \leq x \leq \sqrt{3}## However the book gives another solution which is ##-1 \leq x \leq...
  12. R

    Absolute Uncertainty of a Negative Power

    1. Determine the relative and absolute uncertainties of R-2 if R is measured to be 4.5 ± 0.005 m 2. The attempt at a solution So according to what I know so far, multiplication and division of uncertainties requires the addition of relative uncertainties... First I tried to get the...
  13. T

    Fortran FORTRAN 77 input absolute values

    How to input absolute values in FORTRAN77? This was the code I used READ *,H PRINT *,H The input I gave was 0.01 But the output I got was 0.00999999978.
  14. P

    Why no absolute derivative in this example of geodesic deviation?

    On the surface of a unit sphere two cars are on the equator moving north with velocity v. Their initial separation on the equator is d. I've used the equation of geodesic deviation...
  15. Dethrone

    MHB Absolute value within absolute value

    I did this question two ways, each of which yielded a different answer. I'll post method one first. $$\left| (2|x-3|-5|x+4|) \right|$$ Sign changes occur when $x<-4$, $-4<x<3$, and $x>3$ If $x<-4$, then $|3x+26|>4$, and so $x>-22/3$ and $x<-10$. Clearly since $x$ much be less than $-4$, only...
  16. Julio1

    MHB Can Absolute Value Solve the Problem of Convergence for Inverse Functions?

    Show that if $y_0\ne 0$ and $|y-y_0|<\min\left(\dfrac{|y_0|}{2},\dfrac{\varepsilon|y_0|^2}{2}\right)$, then $y_0\ne 0$ and $\left|\dfrac{1}{y}-\dfrac{1}{y_0}\right|<\varepsilon.$
  17. RJLiberator

    Help me proove absolute value inequalities and Solve an Integral

    1) True or Fale? |a-b| \geq ||a|-|b|| My solution: I broke this up into 4 different cases. 1. a> 0 b>0 2. a<0 b<0 and so on... For each case, I ended up with a more simplified version of the inequality. For instance, in case 1 where I used a<0 and b<0, I ended up with the simplified statement...
  18. Dethrone

    MHB Definition of a derivative - absolute value

    \d{}{x}\frac{1}{\sqrt{x}} by the definition of the derivative. $$\lim_{{h}\to{0}}\frac{\frac{1}{\sqrt{x+h}}-\frac{1}{\sqrt{x}}}{h}=\lim_{{h}\to{0}}\frac{\sqrt{x}-\sqrt{x+h}}{h\sqrt{x^2+2xh}}=\lim_{{h}\to{0}}\frac{x-(x+h)}{h\sqrt{x^2+2xh}\left(\sqrt{x}+\sqrt{x+h}\right)}$$ Setting $h=0$...
  19. A

    MHB What are the solutions to this absolute value equation?

    I have trouble solving this equation |1/2x+1|=|x| My answers are x=2 and x=-2/3
  20. N

    Examine the continuity of this absolute value function

    Homework Statement y = 1-abs(x) / abs(1-x) The Attempt at a Solution For x < 0, abs(x) = -x y = (1+x) / -(1-x) = -(1+x)/(1-x) I stopped here because this is the part I got wrong. For x < 0, my solutions manual got (1+x) / (1-x). What did I do wrong?
  21. Dethrone

    MHB Absolute values in Integration

    I feel like I'm asking the weirdest questions that most people don't ask, but here it is. Suppose we have this integral (I made it up): $$\int \sqrt{x^4+2x^3+x^2}$$ Now, I feel most people would say the answer is simply, $\frac{1}{3}x^3+\frac{1}{2}x^2+C$. But technically, that is only true...
  22. M

    Trouble with needless of absolute value

    Hi, while solving differential equations problems we have to sometimes use absolute value while taking an integral of which 1 over a function. But in some problems I understand that we do not have to use absolute value sign for example if the function related with atom number which can...
  23. K

    Power series absolute convergence/ Taylor polynomial

    1. What if absolute convergence test gives the result of 'inconclusive' for a given power series? We need to use other tests to check convergence/divergence of the powerr series but the matter is even if comparison or integral test confirms the convergence of the power series, we don't know...
  24. Dethrone

    Understanding integration with trig identities, and absolute value

    Homework Statement In integration, we are allowed to use identities such as sinx = \sqrt{1-cos^2x}. Why does that work, and why doesn't make a difference in integration? Graphing \sqrt{1-cos^2x} is only equal to sinx on certain intervals such as(0, \pi) and (2\pi, 3\pi). More correctly...
  25. Dethrone

    MHB Integration with trig identities and absolute value

    In integration, we are allowed to use identities such as sinx = \sqrt{1-cos^2x}. Why does that work, and why doesn't make a difference in integration? Graphing \sqrt{1-cos^2x} is only equal to sinx on certain intervals such as (0, \pi) and (2\pi, 3\pi). More correctly, shouldn't we use the...
  26. Mogarrr

    Integrating functions with absolute values

    To find E |X| of a cauchy random variable, I need to integrate \int_{-\infty}^{\infty}\frac1{\pi}\frac{|x|}{1+x^2}dx . From the definition of absolute value, we have \int_{-\infty}^0\frac1{\pi}\frac{-x}{1+x^2}dx + \int_0^{\infty}\frac1{\pi}\frac{x}{1+x^2}dx (I think). But, the very next...
  27. A

    MHB Basic Calculus II Integral Questions - Riemann Sums, Absolute Integrals, etc.

    Hey guys, I'd appreciate some help for this problem set I'm working on currently The u-substitution for the first one is somewhat tricky. I ended up getting 1/40(u)^5/2 - 2 (u) ^3/2 +C, which I'm not too sure about. I took u from radical 3+2x^4. For the second question, I split the integral...
  28. C

    Derivatives involving the Absolute Value of Functions

    Problem: y = ln|sec(x) + tan(x)| Attempted Solution: See Attachment I was hoping someone could identify my error and possibly write it out for me. At first I thought my steps were correct and everything was in order. However, when I checked my answer on WolframAlpha it gave me a slightly...
  29. Y

    MHB Absolute Min-Max over a region

    Hello, I am trying to find the absolute min-max of the function: \[f(x,y)=xy^{2}\] over the set: \[D=x^{2}+y^{2}\leq 1, y\geq 0, x\geq 0\] Usually, when I have a problem where D is a rectangle, I check every line out of 4 for min-max. If D is a triangle, the same. If D is a circle, I...
  30. T

    Specific Heat in Absolute vs Relative Units

    I'm running a simulation on a gas mixture that spits out its Specific Heat in a number of different units. The values for Specific Heat in Btu/lbmolF vs Btu/lbmolR are the same, which confuses me at first glance. I sort of remember in Thermo not having to worry about Btu/lbmolF vs...
  31. AotrsCommander

    How to calculate absolute magnitude of a stellar body?

    I'm trying to find the appropriate formula (and abstractions to plug into it as necessary) to work out the absolute magnitude (from which I can dervive an apparent magnitude) of a solar body. I've found a lot of formula which relative absolute and apparent magnitude, but trying to find how to...
  32. B

    MHB Absolute Value Graph: Explaining |2-x| Horizontal Translation Right

    Can someone explain to me why |2-x| would have a horizontal translation to the right? When I've always been taught that anytime you see a [+] it will translate to the left. The graph would be a regular |x| graph but it is shift 2 spots to the right. Thanks to anyone for help
  33. S

    Calculation of absolute electrode potential and salt bridge qns

    >According to http://www.chemguide.co.uk/physical/redoxeqia/introduction.html each electrode has an absolute electrode potential which is the difference between the positiveness and negativeness. So if we had a Zn plate in water and it has a negative charge of -5 on the metal. Would the absolute...
  34. D

    Inequality with absolute values

    Wonder if this is true or just mistype: |x+y| \leq |x| +|y| If this is true how to proof because cannot find it out anywhere written Regards
  35. K

    Rotating pendulum. Find absolute acceleration

    Homework Statement I have to find current absolute acceleration in attached picture in points 1,2,3,4 and draw vectors. The picture is rotating pendulum. The rest data show attached picture: Homework Equations aabs = arel + au + acor acor=2*angular velocity X vrel The Attempt at a...
  36. MarkFL

    MHB Solve Definite Integral w/ Absolute Value Factor - Yahoo! Answers

    ☺'s question at Yahoo! Answers: a definite integral whose integrand has an absolute value factor. Here is the question: I have posted a link there to this thread so the OP can view my work.
  37. J

    Is There a Function That Always Results in a Positive Sign?

    "Geometric absolute" If exist a function called absolute that ensures that the result have always the posite sign, so, exist some function that ensures that the sign of the result is always ×? ##f(x) = x## ##f(\frac{1}{x}) = x##
  38. B

    When is the root of a number both negative and positive?

    Homework Statement I have a simple problem with roots and absolute values. When is the root of a number both negative and positive? Is only the equation of a number say f(x) = √x both the negative root and the positive root? Homework Equations If a = 1; b = -2, och x = a2√(ab-b2+2) Why is x...
  39. R

    MHB Absolute stability of finite difference scheme

    The Finite difference scheme: \begin{equation} y_{n+3}-y_{n+1}= \frac {h}{3}(f_{n}-2f_{n+1}+7f_{n+2}) \end{equation} Deduce that the scheme is convergent and find its interval of absolute stability(if any) => the first characteristic polynomial is then \begin{equation} ρ(r)= r^3 -r...
  40. Q

    Kinetic energy relative or absolute?

    Hello folks! I have just come from a night at the pub with fellow students of life where over many a pint several mysteries of the universe were discussed. One of my friends asked me a question concerning special relativity that initially took me by surprise and which has me wondering about the...
  41. mrnike992

    Could there be an absolute 'state of reference?'

    Could there be an absolute 'state of reference' somewhere in the universe, perhaps at the location of the original center? If so, would it have to hold the same frame of reference in each dimension, including time? How would it do so? Looking at the Hafele-Keating Experiment in particular...
  42. S

    Absolute time, local time, planck time

    While Planck time is usually regarded as the shortest unit of time, isn't the shortest unit of time that can exist is the time it took to go from absolute time, the big bang, to everything after that i.e. local time? Did local time exist at the instant of the Big Bang?
  43. T

    Estimating Milky Way Absolute Magnitude

    Important: All Logs are base 10 and not the natural log. Homework Statement This question is from Foundations of Astrophysics from chapter 19 Suppose the Milky Way consisted of 2.7x10^11 stars, each of solar luminosity MB=4.7. What would be the absolute magnitude of the whole galaxy? To...
  44. K

    Can Absolute Value Property be Proven for Real Numbers x and y?

    Homework Statement Prove that for every two real numbers x and y ##|x+y| \leq |x| + |y| ##Homework Equations The Attempt at a Solution There are three cases. The easiest ones is when they are both positive and negative. The third one I have problems with. The numbers have different sign. Say...
  45. T

    How Does Material Choice Impact Physics Experiments on Absolute Zero?

    I just performed a lab in my physics class, and there are a few conceptual questions that I am having trouble with. The lab was simple. We took a constant volume sphere made of Stainless steel and filled with air. We changed the temperature of the water it was into record the corresponding...
  46. T

    Calculating Absolute Velocity at 50% the Speed of Light

    In the spirit of this forum I should first announce: -generally, I have no idea what I'm talking about but look for you folks to enlighten me. Question: If I am traveling at a significant fraction of the speed of light and I wish to know my current absolute velocity can I use the speed of...
  47. F

    Model to draw an absolute straight line

    I am looking for information to assist me in designing a model or program to draw a straight line bisecting the universe. Ok maybe just the Milky Way galaxy. I would like to view this line from various points 1. as viewed from a point on Earth (possibly one of the poles) 2. as viewed from a...
  48. 9

    Absolute value and piecewise functions

    Homework Statement Find if continuous and differentiable. I am having problems with the differentiable part. Homework Equations f(x) = x² + 3, |x| ≤ 1 f(x) = |x| + 3, |x| > 1 The Attempt at a Solution (1)^2 + 3 = 4 |1| + 3 = 4 ∴ It is continuous Now, rewriting it, you...
  49. M

    Definite Integral with Absolute Value.

    The problem is ∫x^2 - 3x - 5 with the lower limit being -4 and the upper limit 7. I broke the integrals into three parts from [-4, -1.1926], [-1.1926, 4.1926], [4.1926, 7] I did the integral and got (x^3)/3 - (3/2)x^2 - 5x I subbed in the lower and upper limits and got 32.861 for [-4...
  50. E

    Question about absolute value limits?

    When do you check the limit from the right and left of a limit with an absolute value in the numerator or denominator? For example, why do you check the limit from both sides of: Lim x -> 3/2 (2x^2-3x)/absolute value(2x-3) But only the left side of: limit as x approaches -2...
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