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. J

    Absolute pressure at an ocean depth

    a) Calculate the pressure at an ocean depth of 550 m. Assume that the density of sea water is 1022 kg/m3 and that the air above exerts a pressure of 101.3 kPa. b) At this depth, what force must the frame around a circular submarine porthole having a diameter of 32.0 cm exert to counterbalance...
  2. H

    Definite integrals of absolute values

    Homework Statement \int|x^{2}+x-2|dx from -2 to 2 Homework Equations The integral of f(x) from a to b = F(b) - F(a) |x| = { x if x >= 0; -x if x < 0 --- Ok, I don't know how to do the definite integrals of absolute values.. was never shown an example of it in class, but I kind of...
  3. A

    Absolute Value in a double integral

    [SOLVED] Absolute Value in a double integral Homework Statement If \Omega = [-1,1] x [0,2], evaluate the double integral \int\int_{\Omega} \sqrt{|y-x^{2}|} dA given that it exists. Homework Equations None The Attempt at a Solution I know that in order to integrate with the...
  4. rocomath

    Analysis of "Absolute Convergence" of $\sum_{n=2}^{\infty}\frac{1}{(lnn)^{n}}$

    \sum_{n=2}^{\infty}\frac{1}{(lnn)^{n}} If I treat it as a geometric series, then when n=3, r is smaller than 1 \sum_{n=2}^{\infty}(\frac{1}{ln3})^3 What matters is that it's ultimately decreasing, would that be the correct approach? Even problem, no answer! Thanks.
  5. K

    Mean Absolute Deviation/Standard Deviation Ratio

    I ran across an interesting statistic today while doing some research, but it was stated as a matter of fact without explanation and there appears to be a dearth of material on it. It was stated that the Mean Absolute Deviation ("MAD") of a Normal (Gaussian) Distribution is .7979 of a Normal...
  6. W

    Why is f(x,y) not differentiable at (0,0)?

    Hello, My question is as follows: Show that the function f(x,y) = sqrt(abs(xy)) is not differentiable at (0,0). I was going to go with trying to show that the directional derivatives don't all exist here, but that would require finding the gradient, and I always get confused when trying to...
  7. J

    Absolute value of a complex number

    Homework Statement Find the real/imaginary parts of sinh(x+yi) and its abs value.Homework Equations The Attempt at a Solution I am able to decompose sinh(x+yi) = cosy*sinh(x) + isin(y)cosh(x) - (which is correct according to my book) Now finding the absolute value is kind of causing some...
  8. D

    Does Absolute Zero Occur in the Universe?

    I am not sure if I should be posting this in another section, but my question is this: Does the uncertainty principle necessarily prevent a temperature of absolute zero occurring anywhere in the universe? I am no physics expert, just curious really. Liam
  9. C

    Absolute Convergent Series proof

    Homework Statement Let Sumation "a sub n" be an absolutely convergent series, and "b sub n" a bounded sequence. Prove that sumation "a sub n"*"b sub n" is convergent. (sorry fist time on this site and can't use the notation.) Homework Equations Theorem A: that states sumation "a sub n"...
  10. H

    Understanding Negative Absolute Temperature: Myth or Reality?

    What is really meant by temperature and negative absolute temperature? Is that an abnormal state that happens during population inversion in laser?
  11. B

    Absolute Max/Min of y = x^2 * e^-x on [-1,3]

    Homework Statement Find the absolute max/min on [-1,3] for y = x^2 * e^-x Homework Equations The Attempt at a Solution F'(y) = (2x)(e^-x) + (x^2)(e^-x) = xe^-x(2 + x) x = 0, -2 (Critical Points) F(-2) = 29.56 MAX (CP) F(-1) = 10.87 F(0) = 4 F(3) = 0.199 MIN...
  12. B

    Absolute Value of a Difference with Heaviside Function

    Homework Statement If |x| = -x + 2x*H(x) what is |x - a|? This isn't the actual question, just something I need to know to solve the question. Homework Equations H(x) is the Heaviside function which is: y = 1 if x >= 0 y = 0 if x < 0 The Attempt at a Solution Well, I'm...
  13. C

    How do I graph the absolute value function with multiple layers?

    Homework Statement The problem is: Draw the graph of the following function: f(x)=|x+|x+|x-1||| Homework Equations |x|=\left\{\begin{array}{cc}x,&\mbox{ if } x \geq 0\\-x,&\mbox{ if }x<0\end{array}\right The Attempt at a Solution If the function were, for instance...
  14. F

    Exploring Voltage at Absolute Zero

    Hi, I'm currently doing an A level course in Physics, so this thought struck me then. I was looking at a simple problem, when a thought struck me, if V=I/R and at absolute zero (0 kelvin) there is no resistance, what happens to the voltage? In other words, V=I/0 I know that you cannot...
  15. B

    Exploring Absolute Zero - Thermodynamic Implications

    Hello all This question is probably a bit ridiculous, but here goes: Hypothetically, If any given closed system has obtained absolute zero temp, does any media (time, gravity, events)occur within? Thermodynamically, Wouldn't this be a state of infinite entropy? Can anyone describe such a...
  16. J

    Absolute max and absolute min problem

    Homework Statement Find the absolute maximum and absolute minimum values of f(x) = (x - 1)^2/3 on [0,2]. Give reasons for your answer Homework Equations None The Attempt at a Solution I first differentiated the function and got. \frac{2}{3}x(x - 1)^{\frac{-1}{3}} that is to...
  17. M

    Trying to understand absolute uncertainties in geometric shapes

    I've been studying absolute uncertainties and do not understand any of it. If someone can explain it will really help. Especially with uncertainties including diameters and area.
  18. B

    Finding the distance modulus and the absolute magnitude

    Homework Statement If a star has an apparent magnitude of -.4 and a parallax of .3'' what is : a) the distance modulus b) the absolute magnitude Homework Equations m is the apparent magnitude and M is the absolute magnitude m-M =5 log d - 5 M= m + 5+5 log(pi''), pi'' is the parallex angle...
  19. F

    Derivatives of absolute values

    Homework Statement Where is the function f(x) = |x| differentiable? Homework Equations [f(x+h) - f(x)] / h The Attempt at a Solution I know that the graph of f(x)=|x| shows a corner at the origin from which 2 lines project at opposite slopes, as in they are symmetric about the...
  20. T

    Discrete Mathematics Absolute Value Proof

    Homework Statement Prove the following statement: For all real numbers x and y, |x| times |y| = |xy| Homework Equations I really don't know how to start this as a formal proof. The Attempt at a Solution I was thinking I'd have to break it down into four cases and logically prove...
  21. U

    How Can I Write an Absolute Value Function for the Outline of the Khufu Pyramid?

    Okay, we don't understand this and we need much help the largest pyramid included in the first wonder of the world is Khufu. IT stands 450 feet tall and its base is 755 feet long. Imagine that a coordinate plane is placed over side of the pyramid. In the coordinate plane, each unit...
  22. A

    [Thermodynamics (More like fluid actually)], Calculating absolute pressure

    Homework Statement http://img409.imageshack.us/img409/771/fluidcm5.jpg Homework Equations F1/A1 = F2/A2 Pressure = Density * Height * Gravity The Attempt at a Solution I do not have a clue of how to solve this problem. Can anyone start me off and provide me couple of hints?
  23. L

    Big Bang and absolute simultaneity

    I was wondering does the notion that the universe is expanding uniformly means there is no absolute rest, but there is absolute simultaneity?
  24. B

    Problems relating to Absolute Continuity

    Hi, it's been awhile since I have studied Lebesgue measure so I'm trying to re-learn the material on my own. Most of my friends don't remember much as well so it's been a bit of a struggle trying to work on these problems on my own. Thank you for any kind of help! OMIT Question 1. If...
  25. L

    A weird absolute value problem

    Please help me out here with this problem: 37. Express the function f(x)=l x l + l x-2 l without using absolute value signs. Okay, I've took a sneak peak at the answer key and it is given in kinda of like piece-wise notation where they have 3 equations and different intervals of x for...
  26. K

    Absolute Convergence: Determining Convergence of (-1)^k*2^n/n^(n/2)

    I just want to verify my answers. I am asked to determine whether the sum converges absolutely, conditionally or diverges. ((-1)^k)*2^n)/n^(n/2). I got that it was conditionally convergent, is that correct?
  27. R

    Absolute Values and Continuous Functions

    Homework Statement We recently proved that if a function, f, is continuous, it's absolute value |f| is also continuous. I know, intuitively, that the reverse is not true, but I'm unable to come up with an example showing that, |f| is continuous, b f is not. Any examples or suggestions would...
  28. D

    Absolute Value Integrals

    Hi. For an integral like this, for example: \int {\sqrt {1 - \cos ^2 x} dx} The most obvious way of solving would be to make use of the pythagorean identity, to get: \int {\sqrt {\sin ^2 x} dx} Now, I've been taught to simply evaluate it like this: \int {\sqrt {\sin ^2...
  29. Z

    Trig integrating with absolute values:

    Homework Statement \int_0 ^\pi \sqrt{1-\sin^2 x} dx Homework Equations 1 - \sin^2 x = \cos^2 x The Attempt at a Solution I don't know how to treat this since cos changes sign half way across the integral. I know the answer should be 2 but I keep getting 0 every which way I try.
  30. M

    To measure nature with absolute certainty -

    MEASURE To measure nature with absolute certainty, one would need a tool of absolute certainty. Unfortunately for science, there is no such thing! Measure? MJA
  31. M

    Derivative absolute value and also curve help

    Hey i have 2 questions here that i have finished and i have no answers to my solutions so i would like someone to check it over and see where i went wrong , I am not 100% sure on this stuff and need some help , thanks a lot ! Question 1: Using the definition of a derivative, show that ƒ (x) =...
  32. S

    Cooling Near Absolute Zero: What's Used?

    I am aware that absolute zero can not be achieved by cooling a substance since absolute zero is zero-point energy. I was just wondering what is used (coolant wise and apparatus wise) to cool something near this temperature since there some experiments such as the Boise-Einstein Condensates which...
  33. P

    How can you calculate density from : altitude temperature and absolute humidity

    How can you calculate density from : altitude temperature and absolute humidity
  34. B

    Absolute Magnitude Homework: Mass 3.5x Sun, Luminosity 42.9x Sun

    Homework Statement A star is 42.9 more luminous than our Sun and has a mass 3.5 times bigger than the Sun. Assuming our Sun has an Absolute Magnitude of 4.83 what would the Absolute Magnitude of this star be? Homework Equations The Attempt at a Solution
  35. P

    At Absolute Zero: Examining He Atom Universes

    If the universe consisted only of He atoms and all of them are in the ground state, does it imply this universe has 0 or close to 0 kelvin? It is only the deexcitation of the outer electron emitting a photon which can produce any significantly measurable heat in the universe?
  36. moe darklight

    How are materials brought to (near) absolute zero?

    Hey, an article on the new Discover Mag talks about underground labs trying to detect dark matter. It mentions that the sensors have to be brought down to almost near absolute zero... I then realized that, even though I keep reading about things being put in extremely low temperatures, I have no...
  37. S

    Absolute Magnitudes for Cepheids

    Would somebody help me in entering a calculation into my scientific calculator? The equation is Mv = - [2.76 log10(P) – 1.0)] – 4.16 I have the value of P but I'm not sure how to enter this into the calculator. I get a different answer every time. Thanks,
  38. Simfish

    Converting Relative URLs to Absolute URLs

    Within all pages within a folder. So I downloaded a number of pages that have links to pages that I want to download (using a utility such as HTTrack or DownThemAll). The problem is that the URLs of the pages are all relative, so when I save the pages to an external server (I have to do that...
  39. D

    Possible Values of a and b for |2x+a| = |b-x| at x=-4 and x=2/3

    The equation |2x+a|=|b-x| has exactly 2 solutions, at x=-4 and x=2/3. Find the value(s) of a and b. Ok so the questions is asking me to find possible values of a and b which make the equation true for ONLY x=-4 and x=2/3. So for: |a-8|=|b+4| |a+4/3|=b-2/3| I need to find the values...
  40. C

    Learn C/C++ Programming: A Beginner's Guide

    hi i simply know nothing about programming languages and related stuff, but i really want to learn one, c or c++, i don't know where to start can you please tell what to do and where to start, websites, books... please help:cry: i appreciate ur help thanks:smile:
  41. D

    Absolute Value functions => Piecewise Function

    Given the function: f(x) = \left| {x + 1} \right| + \left| {x + 2} \right| How can i write that as a piecewise function? If i was given something in the form of f(x) = \left| {g(x)} \right|, i know to write it as: f(x) = \left\{ {\begin{array}{*{20}c} {g(x),} & {g(x) \ge 0}...
  42. K

    Is the intellect the absolute reference frame?

    Hi I know that the following can never be done in the real world, but in theory, if the vectors of all particles, antiparticles, photons etc. in the universe could be summed, would that qualify as an absolute reference frame for that instant in time? Clearly each instant would have a...
  43. M

    Absolute Zero: Understanding Heat and Molecular Vibrations

    I've been told that heat is vibrations of the molecules. I see two ways to reach absolute zero -273,15 C 1. you could stop all the molecules so that they wouldn't move at all. or maybe?? 2. remove all the molecules. No molecules no vibrations no heat?? is no 2. possible?
  44. S

    Max of the absolute value of a polynomial

    What I have is this: Let P_n(x)=(x-x_0)(x-x_1)...(x-x_n), _i are subscripts. Prove that the maximum value of |P_1(x)| for x in [x_0,x_1] is h^2/4, where h =x_1 - x_0. All the x_i terms are evenly spaced. That is, x_(i+1)-x_i is the same for all i. What I noticed is that P_1(x_0)=P_1(x_1)=0...
  45. T

    How do I graph an absolute value inequality in 2 variables?

    I need some help graphing an Absolute value. I know what it look like from a graphing calculator but I don't understand how to get to the answer. http://media.twango.com/m1/original/0042/5fda15431b96400eb32e66afa3627624.jpg Thanks
  46. A

    Why is the sign reversed on -4 in solving 3x^{2}+12x>0?

    I'm confused by why my work is wrong: 3x^{2}+12x>0 3x(x+4)>0 3x>0 , x+4>0 x>0 , x>-4 However, the correct answers are: x>0 and x<-4? Why is the sign reversed on -4? I thought you were only suppose to reverse it if you multiply or divide the equation by a...
  47. A

    Absolute Convergence of z: \mathbb{N}^2 to \mathbb{C}

    Let z : \mathbb{N}^2 \to \mathbb{C}. Suppose that: 1) for all natural n, \sum _{j \in \mathbb{N}}z(n,j) converges absolutely. 2) for all natural j, \sum _{n \in \mathbb{N}}z(n,j) converges absolutely. 3) \sum _{n \in \mathbb{N}}\left (\sum _{j \in \mathbb{N}} z(n,j)\right ) converges...
  48. Loren Booda

    Have absolute gravitational singularities ever formed?

    What of the possibility that dark energy prevents total gravitational collapse of black holes, and might also have helped avoid an actual singularity at the big bang?
  49. O

    Estimate Mass H2O Vapor in 1 m^3 Air at +20°C

    Homework Statement Estimate the mass of water vapor that is contained in 1 m^3 of saturated air at a temperature of plus 20 degrees Celsius 2. The attempt at a solution I looked up the saturation pressure for water vapor at the given temperature. Can I just use the ideal gas-law for the...
  50. R

    Definition of Absolute Value of a Function

    Homework Statement Question straight off the book "In this lesson, you have explored the absolute value of a function. How is it defined?" Homework Equations In this lesson, I did questions like xE[0,9] and was told to write each intervals in absolute value notation. The Attempt at a...
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