Absolute Definition and 1000 Threads

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. W

    Express with at least one less pair of absolute value signs

    We have ## ||a+b|-|a|-|b|| ##. The only way I can think to eliminate one pair of absolute value signs is to consider the cases separately and determine which pair(s) can be removed without affecting the final answer. I'm trying to get better at doing these types of problems, so feel free to...
  2. SSGD

    Crystal Structure of Metals at Absolute Zero, Waves

    I have been trying to find information on the crystal structure or phase of solid elemental metals at temperatures close to absolute zero, but I can only find information on there ambient structures. Does anyone know of any sources that would have thermodynamic tables for solid metals at low...
  3. paulmdrdo1

    MHB How do you define absolute value function on different intervals?

    Define f(x)= |x+3|-|x-3| without absolute value bars piecewise in the following intervals (-∞,-3);[-3,3);[3,+∞). this is how i do the problem, I removed the absolute value bars first f(x)= x+3-x+3 = 6 now i don't know how to define it piecewise. can you show me how define it correctly. thanks!
  4. M

    Absolute Exponential Integration

    Hello! What is the integration of the absolute value of e^ix? That is what is ∫|e^ix|^2 equal to? The whole absolute thing got me lost. Thanks in advance.
  5. S

    How Does Absolute Pressure Differ from Gauge Pressure?

    The formula for absolute pressure is absolute P=gauge P+atmospheric pressure. So when the gauge is at 0 it's actually 1 atm. So using the gas law if I were to half the volume the pressure would increase to 2 atm. So would the gauge read 1 atm when this happens? So how does the mechanism...
  6. P

    How to solve an absolute value integral?

    Homework Statement ∫0-->x |t|dt Homework Equations // The Attempt at a Solution 1/2*x^2 for x>= 0 1/2*(-x)^2 for x<= 0 Not sure what to do to be honest. (the answer in the back of the book says 1/2*x|x|).
  7. M

    Confused on how the absolute value changes the method of deriving

    Homework Statement Find derivative of abs (2x^3 + 8x^2 + 5x +1).Homework Equations The Attempt at a Solution A little confused on how the absolute value changes the method of deriving that equation. When I derive it normally, I get (6x^2+16x+5).
  8. Petrus

    MHB Absolute Value: Solve for x | MHB

    Hello MHB, solve ||x|-2|+|x+1|=3 and we find that x=0,-2,2,-1 I got problem to find the 'case', Regards, |\rangle
  9. C

    Could absolute motion exist in higher dimensions, if they exist?

    If the universe follows a 3-torus or finite unbounded shape, or we are situated on the surface of a 4D sphere, then the 'centre' if the universe will exist. If one could locate the position of this origin in 4D space, and remain stationary with respect to it, then would that object be at...
  10. G

    Absolute value of complex exponential equals 1

    Hello all, I'm having trouble showing that |e^it|=1, where i is the imaginary unit. I expanded this to |cos(t)+isin(t)| and then used the definition of the absolute value to square the inside and take the square root, but I keep getting stuck with √(cos(2t)+sin(2t)). Does anyone have any...
  11. Q

    Derivative of inverse trig function absolute value?

    Find the derivative of y = arctan(x^(1/2)). Using the fact that the derivative of arctanx = 1/(1+x^2) I got: dy/dx = 1/(1+abs(x)) * (1/2)x^(-1/2) But my textbook gives it without the absolute value sign. I don't understand why because surely x^(1/2) squared is the absolute value of x...
  12. H

    Uncertainty of experiment relative or absolute

    I calulated the time(s), then i found the uncertainty as a percentage of my results. Later on i calculated 1/time and used the uncertainty % which i originally calulated. Could somebody tell me if it is relative or absoulte uncertainty and why?
  13. C

    Absolute convergence proving that limit =1

    Homework Statement limit as k--> infinity ABS VALUE((cos(pi*k+pi))/(cos(k*pi))) Homework Equations The Attempt at a Solution Can someone prove to me why this limit is equal to 1? I have tried several other sources and I have not had any luck.
  14. N

    Determine the absolute Velocity and Acceleration of Particle A

    Homework Statement The disk rolls without slipping on the horizontal surface, and at the instant represented, the center O has the velocity vO = 2.2 m/s and acceleration aO = 5.5 m/s2 with directions shown in the figure. For this instant, the particle A has the indicated speed u = 3.2 m/s and...
  15. T

    Absolute value squared of complex number?

    I'm given 1-a\cdot e^{-i\cdot 2 \pi f}. The squared absolute value apparently is |1-a\cdot e^{-i\cdot 2 \pi f}|^2=1+a^2-2acos(2 \pi f). Sadly the awnser doesn't show the steps of this derivation. I have tried many times to derive it my self but have not been able to do so. I feel like i...
  16. MarkFL

    MHB F's question at Yahoo Answers involving absolute extrema

    Here is the question: Here is a link to the question: Math Question - Calculus!? - Yahoo! Answers I have posted a link there so the OP can find my response.
  17. P

    Solving an absolute value inequality

    Homework Statement lx/(x-2)l < 5 Homework Equations The Attempt at a Solution x/(x-2) < 5 x< 5x-10 10 < 4x 5/2 < x x/(x-2) > -5 x > -5x+10 6x > 10 x > 5/3 The answer is x < 5/3 and x > 5/2 so where did I go wrong on the second one?
  18. W

    Absolute and Conditional Convergence Tests for Series | Homework Equations

    Homework Statement Absolute, Conditional, - convergence, or Divergence.Homework Equations \displaystyle \sum^{∞}_{n=1} (-1)^n e^{-n} The Attempt at a Solution 1. Alternating Series Test 2. Ratio Test for ABsolute Convergence 1. \displaystyle (-1)^n (1/e)^n an > 0 for n=1,2,3,4 - YES...
  19. PhizKid

    Predicting the temperature of absolute zero experimentally

    Homework Statement A metal ball with pressure gauge at room temperature and standard pressure is immersed into three different liquids each with different temperatures in succession (the three liquids are alcohol in dry ice, boiling water, and freezing water), and then is immersed into these...
  20. T

    Is angular frequency absolute?

    In classical mechanics, is the angular frequency of a rotating object, planetary system etc. the same as viewed from any inertial reference frame?
  21. N

    Find the angular velocity of the Absolute Motion System

    Homework Statement Point A is given a constant acceleration a to the right starting from rest with x essentially zero. Determine the angular velocity w of link AB in terms of x and a. I have attached an image of the question Homework Equations w = θ' α = θ'' Pythagoras and trig...
  22. P

    Definite Integral of Absolute Value Function (Calc I)

    Homework Statement $$\int_{0}^{\ 2\pi} \ |e^{sin(x)}cos(x)| \, dx$$ I know that it simplifies to $$ 2e- \frac{2}{e} ≈ 4.7 $$ I'm not sure how to approach this problem. Do I just break the integral up into the domains where it's positive and negative and integrate each component...
  23. Petrus

    MHB How to Find Max and Min Points for \(\frac{x^3}{2} - |1 - 4x|\) in \((0, 2)\)?

    Calculate max and min point to function \frac{x^3}{2}-|1-4x| in the range \left(0,2 \right) I got one question, shall I ignore when it's \frac{x^3}{2}-(-1+4x) cause then x<0 and that don't fit in my range? Do I got correct?
  24. E

    Gradient of an absolute value raise to a power

    Homework Statement Show that ∇_{x}|x-y|-3= -(x-y)|x-y|-3 x and y are vectors.Homework Equations The Attempt at a Solution When dealing with just a straight up absolute value I know that a solution can be found by using a piece wise approach, but I don't think that's what I should be using...
  25. A

    What is the Absolute Value of an Exponential with Complex Exponent?

    I want to calculate |e^{a^{2} + \frac{it}{m\hbar}}|^{2} i is imaginary unit. my trie: a^{2} + \frac{it}{2m\hbar} is a complex number so its module is: \sqrt{a^{4} + \frac{t^{2}}{m^{2}\hbar^{2}}} = \sqrt{a^{4}(1 + \frac{t^{2}}{m^{2}\hbar^{2}a^{4}})} a^2\sqrt{1 +...
  26. E

    Can you please teach me the properties of absolute values

    I am new in the field of science please can you help me. I would I appreciate it. I am not that knowledgeable.
  27. K

    Question about Helium at absolute zero

    At absolute zero, I understand that atoms have a minimum vibration (the atoms are not completely still). Because of this minimal vibration, He atoms can not freeze at absolute zero. But if enough pressure is applied, the liquid then becomes a solid. Does the pressure eliminate or reduce the...
  28. I

    Confused About Squareroots & Absolute Values

    $${ x }^{ 2 }=4\\ \sqrt { { x }^{ 2 } } =\sqrt { 4 } \\ |x|=2$$ According to my professor, in the above case, the absolute value gives two solutions: ##x=±2## Consider the discriminant in the quadratic formula: $$x=\frac { -b±\sqrt { { b }^{ 2 }-4ac } }{ 2a } \\ Let\quad { z }^{ 2 }={ b }^{ 2...
  29. R

    Finding absolute extrema with only 1 critical point

    Homework Statement Edit: Not absolute, just extrema I've already found the critical point to be (-1/2, -1/4, 1/2) with a value of -1/2. My only problem is finding whether this is a max or min. What technique do I use to find out? I don't believe I can use the 2nd derivative test because all...
  30. R

    What are the absolute extrema of the given function on the given set?

    Homework Statement Find the absolute extrema of the function on the set D. f(x,y)= x^2 + 4y^2 + 3x -1 D= {(x,y) l x^2 + y^2 ≤ 4} Homework Equations The Attempt at a Solution The only thing I've done so far was find the critical point. I found f-sub x = 2x+3 and f-suby= 8y...
  31. anemone

    MHB Solving Absolute Value Equations

    Solve the system below: $\displaystyle |x+y|+|1-x|=6$ $\displaystyle |x+y+1|+|1-y|=4$ I've solved this problem and my intention is purely to gain another insights on how others would approach it and I surely hope you find this problem as an interesting one!:)
  32. D

    Confused about mole ratio being relative or absolute

    Let's start with a generalized example: 3A + 1B -> 2C For the mole amount next to each molecule, am I always to consider these as relative to one another or absolute? Most of the videos I have seen are describing the above as "for every 3 moles of A and 1 mole of B you get 2 moles of C". I...
  33. J

    What is the reason for absolute zero temperature?

    What is the empiric reason behind the assumption that there is lowest thermodynamic temperature (absolute zero)? And that all other temperatures of bodies in thermodynamic equilibrium are always higher ? I am looking for a reason not using the entropy concept, as the entropy was derived...
  34. M

    Subspace of R2 involving absolute value

    Homework Statement {(x1,x2)T| |x2|=|x2|} So my first thought is we would have to check for both cases (x1,x1) and (-x1,-x1) a=(x1,x1)T b=(v1,v1)T βa=(βx1,βx1)T for the case where a<0 βa(-βx1,-βx1)T thus it is closed under scalar multiplication. a+b=(x1+v1,x1+v1) for the case...
  35. H

    Color Indices and Absolute and Apparent Bolometric Magnitude

    Homework Statement Given: Spherical blackbody with surface temperature of 30000K radius of 6.0 x 10^9 m located 123pc from earth Homework Equations Find the absolute and apparent bolometric magnitudes The Attempt at a Solution My camera needs batteries so I cannot post my work...
  36. C

    Which materials would survive at near absolute zero, intact?

    What would happen to things on Earth if transported to the moon? For instance, say that a house, with furniture and fixtures in place, were dropped gently onto the moon's surface? How about food - meat, vegetables, fruit? Would things crack? Or would they survive the experience so that if...
  37. B

    Setting up an inequality with absolute value

    Homework Statement I need some help setting up this inequality: How accurate do the sides of a cube have to be measured if the volume of the cube has to be within 1% of 216 cm^3 Not very good with word problems and for some reason this course never deals with them until now? And this is...
  38. S

    Absolute Alcohol Vs. Absolute alcohol

    I read in a book that an aqueous solution of ethanol produces a constant-boiling mixture which contains 95.6% ethanol and 4.4% water. This is called rectified spirit. I googled the word "constant-boiling" and I came to the conclusion that it's nothing but azeotrope. But it isn't clear to me...
  39. D

    Evaluating the integral of absolute values

    Homework Statement ∫(0 to 3pi/2) -7|sinx|dx Homework Equations The Attempt at a Solution I am not sure how to treat it as it has an absolute value i assumed that you could remove the -7 to get -7∫|sinx| dx then integrate sinx into -cosx but since there is absolute...
  40. M

    Can you reach absolute zero in complete empty space

    Ok, so I know that the laws of physics say reaching absolute zero temperature is impossible, but suppose we took a box that was perfectly insulated in completely empy space, and I took all the particles out of it to create a vacuum. Now, since there are no particles in the box, then wouldn't...
  41. B

    Can Understanding Gravity Help Us Grasp Absolute Zero?

    Absolute zero is the theoretical state in which a system reaches 0K, or NO energy present right? And if gravity affects everything with momentum and energy, would it cease to affect absolute zero systems because it includes no energy and thus no momentum? I posted a blog post on it here...
  42. S

    Exploring Beyond Absolute Zero: Thermodynamics Re-examined

    http://www.tgdaily.com/general-sciences-features/68525-beyond-absolute-zero-temperatures-get-hotter#cRgTRdxE2qwYX5DR.16 It's been done in the lab, could this be seen in the cosmos? Could this affect entropies end game? What does this mean for the second law of thermodynamics?
  43. julcab12

    Similarities of negative absolute temperature to dark energy?

    “The inverted Boltzmann distribution is the hallmark of negative absolute temperature; and this is what we have achieved,” says Ulrich Schneider. “Yet the gas is not colder than zero kelvin, but hotter,” as the physicist explains: “It is even hotter than at any positive temperature – the...
  44. F

    Quantum Gas Below Absolute Zero

    Quantum Gas Below Absolute Zero! http://www.nature.com/news/quantum-gas-goes-below-absolute-zero-1.12146 I am a fresh undergraduate student and not expertise in fields. The link above shows an interesting research on negative temperature. I've visited wikipedia and found out that negative...
  45. B

    Exploring Negative Temperatures: What Lies Beyond Absolute Zero?

    Absolute zero is often thought to be the coldest temperature possible. But now researchers show they can achieve even lower temperatures for a strange realm of "negative temperatures." http://www.livescience.com/25959-atoms-colder-than-absolute-zero.html
  46. P

    Solving Absolute Value Problem | 3-x=x-3

    I'm currently reviewing pre-calculus material and encountered a little problem with an absolute value expression. |3-x|=x-3 Now the way I learned absolute value expressions was that there's a positive and a negative case. So I got: 3-x=x-3 x=3 and -(3-x)=x-3 gives 0=0. Stupid question...
  47. N

    Is There Any Motion at Absolute Zero?

    Is it possible for motion to exist at 0 Kelvin?
  48. P

    Intuitive reason absolute values are used for transformations in statistics?

    this isn't really homework, but I was just wondering if someone could offer an intuitive reason as to why when random variables are transformed, we use absolute values of derivative of those functions, as opposed to the functions themselves?
  49. S

    How does one measure the absolute velocity of an object?

    It is well-known that the velocity of an object can only be determined in relation to the velocity of another object (the two trains in a station). Einstein's relativity theory limits the velocity of an object to the speed of light; it also been demonstrated that no matter what the velocity of...
  50. Vola

    I can't find the limit absolute value function.

    How find the limit of absolute value function? Hi everybody, I can't find the limit of (abs(x-2)-2)/x as x-->1. I know it's (-1) but I don't see how you get to it. If I take (x-2)>0 I get L=-3,(x-2)<0 I get L=-1. However according to the graph two sided limit does exist and it's (-1)...
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