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. M

    MHB Absolute Value Statements

    Rewrite each statement using absolute values. 1. The distance between x and 4 is at least 8. Work: | x - 4 | > or = 8 Correct? Why must we write greater than or equal to for AT LEAST statements? 2. The distance between x^3 and -1 is at most 0.001. Work: | x^3 - (-1) | < or = 0.001...
  2. M

    MHB How can you rewrite expressions using the definition of absolute value?

    The definition of absolute value states the following: | x | = x when x is > or = 0 | x | = -x when x < 0 I can use the above definition to rewrite expressions that do not contain absolute values. | -sqrt{3} - sqrt{5} | Since the expression in the absolute value is less than 0, we can say...
  3. M

    MHB How Can Absolute Value Definitions Be Used to Rewrite Expressions?

    The definition of absolute value states the following: | x | = x when x is > or = 0 | x | = -x when x < 0 I can use the above definition to rewrite expressions that do not contain absolute values. | x^4 + 1 | Since x^4 + 1 > 0, then the answer is simply the expression itself or x^4 + 1...
  4. M

    MHB Is the Definition of Absolute Value Always True?

    The definition of absolute value states the following: | x | = x when x is > or = 0 | x | = -x when x < 0 I can use the above definition to rewrite expressions that do not contain absolute values. | x - 3 |, where x < 3 If x < 3, then we can say that (x - 3) is less than 0. So, -(x - 3) =...
  5. M

    MHB How do I rewrite expressions using absolute value?

    The definition of absolute value states the following: | x | = x when x is > or = 0 | x | = -x when x < 0 I can use the above definition to rewrite expressions that do not contain absolute values. | 1 - sqrt{2} | + 1 The value 1 - sqrt{2} is less than 0. So, we have -(1 - sqrt{2}) + 1. -1...
  6. GregoryC

    B Absolute zero by definition is "nothing"

    Is absolute zero nothing? Can a quanta exist in nothing? There could be no quantum fluctuations at absolute zero.
  7. AdrianMachin

    Finding the absolute error for equation of total resistance

    Homework Statement Prove the equation for ΔRC. (See the first attachment with the circuit schematic inside) Homework Equations (The equation for RC, in both attachments) The Attempt at a Solution You can see my attempt at a solution in the second attachment. I'm stuck at the step shown in the...
  8. X

    Thompson's Absolute Electrometer

    Suppose that the force needed to push a disc down on top of another disk = weight x g, then the two discs are charged with opposite quantities of electricity, then the weight removed, and still the discs remain together due to the force of attraction between the discs; so then the electric force...
  9. peroAlex

    Absolute Value of Magnetization

    Hello, I'm a student of electrical engineering. This task appeared in one of the past exams. I've been using the procedure I believe should yield the correct result, however, it turns out I was wrong. Could somebody please check out where the mistake lays in my calculations? Homework Statement...
  10. M

    MHB Is it Possible for an Absolute Value Equation to Equal a Negative Number?

    Precalculus by David Cohen 3rd Edition Chapter 1, Section 1.2. Question 68, page 11. Before typing the textbook question, I must say that I have not been able to find a satisfactory answer to absolute value equations that equal a negative number. Question: Explain why there are no real...
  11. T

    Volume of 410kg Bluefin Tuna at 15m Depth: 41854 m3

    Homework Statement A 410kg bluefin tuna rests motionless at a depth of 15m below the ocean's surface. The absolute pressure at this depth is 251,700 Pa. What is the volume of the fish? Homework Equations absolute P=gauge Pressure+atmospheric pressure 1atm=1.03e5Pa P=density x g x height...
  12. Unteroffizier

    Find Absolute Magnitude, distance and "T" of binary star system

    This is the problem given at my basic astronomy course. If I turn it in within a month correctly, I get 10 extra points in the finals. Problem: We have binary star system consisting of Star A and Star B. Astronomers have observed it for 11 years, during which it has moved from point A to point...
  13. M

    Integral of absolute value of a Fourier transform

    Homework Statement Hi guys, I am going to calculate the following integral: $$\int_0^{f_c+f_m} |Y(f)|^2\, df$$ where:$$Y(f)=\frac{\pi}{2} \alpha_m \sum_{l=1}^{L} \sqrt{g_l}\left [ e^{-j(\omega \tau_l - \theta_m)} \delta(\omega - \omega_0) + e^{-j(\omega \tau_l + \theta_m)} \delta(\omega +...
  14. P

    Special Relativity - Is damage absolute?

    1. The problem statement, all variables, and given/known data A car of proper length 12m is being driven at 0.9c through a garage of proper length 6m. The garage has a front and back door. The garage owner, Joe, says that the car will fit inside the garage with no damage to it, albeit for a tiny...
  15. DevonZA

    What is the absolute pressure in a tank measured by a manometer?

    Homework Statement A manometer is used to measure the pressure of a gas in a tank. The fluid used has a the specific gravity of 0.85, and the manometer column height is 55 cm, as shown in figure 3-20. If the local atmospheric pressure is 96 kPa, determine the absolute pressure within the tank...
  16. quickquestion

    I The problem of simulating absolute grip

    Ok, so I'm not even bothering with tire friction simulation anymore. What I'm trying to simulate is a tire that has 100% grip at all times (no lateral velocity.) Now you see that the statement I just made has a contradiction in it...If a car has 4 tires, and if a car is rotating, it is...
  17. H

    I Contradiction in an absolute value property?

    An absolute value property is $$\lvert a \rvert \geq b \iff a\leq-b \quad \text{ or } \quad a\geq b,$$ for ##b>0##. Is this true for the case ##a=0##? I mean if ##a=0, \lvert a \rvert =0## so ##0 \geq b##. But ##b## is supposed to be ##b>0##, so we have a contradiction. How can this property...
  18. N

    I Absolute Power Series: Questions & Solutions

    I've 2 questions 1) Why do we take absolute of the power series? 2) I don't get why the interval of convergence is from -inifinity to +infinity. You can find the problem below.
  19. Dimani4

    I Classical Newtonian Physics: Space & Time Independence

    Hi folks, Tell me please why in classical Newtonian physics one can say that the space and time are independent? But we have equations of motion which clearly show this dependence (x=Vt; x=x0+1/2at^2+v0t). Thank you.
  20. T

    Absolute Uncertainty of 1/d^2 Homework

    Homework Statement Given values and uncertainties of d, find the absolute uncertainty in 1/d^2 (see table attached) Homework Equations I know that if it's a square function the absolute uncertainty will be 2 (delta d) / d but I'm not sure if it's correct for an inverse function. The Attempt...
  21. Mr Davis 97

    I Definition of absolute value

    If we define ##|a| = \sqrt{a^2}##, then why can't we do something like ##\sqrt{a^2} = (\sqrt{a})^2 = a##? Or equivalently ##\sqrt{a^2} = (a^2)^{1/2} = a^{2/2} = a##? Isn't this a contradiction? Also, how would this relate to showing that ##\sqrt{|a|} = |\sqrt{a}|## is true or false?
  22. harpazo

    MHB How to Find the Absolute Extrema of a Function Over a Defined Region?

    Find the absolute extrema of the function over the region R. (In this case, R contains the boundaries.) f (x, y) = 12 - 3x - 2y R: The triangular region in the xy-plane with vertices (2, 0), (0, 1), and (1, 2). I need the steps to guide me through this monster question. I am familiar with...
  23. harpazo

    MHB Relative Extrema vs Absolute Extrema

    In basic terms, what is the main difference between relative extrema and absolute extrema? I know that absolute extrema is more involved but why is this the case?
  24. MathematicalPhysicist

    A question on absolute kelvin temperature scale.

    I was asked in an exam the following question: Q: How is the absolute Kelvin Thermodynamic temperature scale defined ? My answer is the following: A: The absolute zero kelvin thermodynamic temperature is defined as the temperature for which the entropy of the system is zero, i.e ##S|_{T=0} =...
  25. harpazo

    MHB Find Absolute Extrema Over Region R

    Find the absolute extrema of the function over the region R. (In this case, R contains the boundaries.) f (x, y) = 12 - 3x - 2y R: The triangular region in the xy-plane with vertices (2, 0), (0, 1), and (1, 2). I need the steps to solve such a problem. I was told to graph the 3 given points...
  26. S

    Is the idea of negative absolute temperature analogous to a virtual image?

    Is the idea of negative absolute temperature analogous to a virtual image in geometrical optics? I was reading this article about such a negative temperature: http://www.livescience.com/25959-atoms-colder-than-absolute-zero.html It seems to me that since temperature is defined by its...
  27. B

    How to find absolute min/max of f(x)=x^3+3x^2-24x+1 on[-1,4]

    Homework Statement How to find absolute min/max of f(x)=x^3+3x^2-24x+1 on[-1,4] I need to find the absolute min and absolute max. Homework EquationsThe Attempt at a Solution I first took the derivative, reduced, and set it to equal 0 to find crit numbers. x^2+2x-8=0 Factored. (x+4)(x-2) = 0...
  28. mccoy1

    I The absolute value of the frequency in quantum mechanics

    I was reading Bransden's Quantum Mechanics 2nd edition, chapter 2 page 61. There,it says "It should be noted that since E =hv (v for nu), the absolute value of the frequency has no physical significance in Quantum mechanics..." Why is that? Isn't this a contradiction?
  29. N

    B GR lacks absolute space, but what is absolute space?

    GR lacks absolute space, but does Newtonian physics also? If not what does GR lacking absolute space mean? I had thought in Newtonian physics that there existed an absolute space in which Newton's laws are true, and that an inertial frame was a reference frame in relative uniform motion to...
  30. R

    MHB Find Absolute Min and Max

    Hello :) I'm struggling a bit on how I can find steps to solve problems like this, because my mind goes all over the place. Find absolute min and max of f(x,y) = 18-3x+6y on a closed triangular region with vertices (0,0), (6,0), and (6,9). I still struggle with partial derivatives and take a...
  31. J

    I Absolute Energy in General Relativity?

    Let us assume that a spacetime has a global time-displacement symmetry described by a timelike Killing vector field ##\xi^\mu=(1,0,0,0)##. Further assume that we have a particle with four-momentum ##P^\mu=m\ V^\mu##. It is well-known that a stationary observer with four-velocity ##U^\mu##...
  32. F

    Understanding Absolute Max Moment: Example and Explanation

    Homework Statement In the first 2 notes , i was told that the absolute max moment will occur under the largest force lying nearest the resultant force of system . but , in the example that i have uploaded , i found that the absolute max moment will occur under the 6kN load instead of 8kN p/ s...
  33. F

    Absolute max shear and moment

    Homework Statement For the maximum moment occur under the 1.5k load , why when we consider the left part of the beam, we just need to consider the forces 2k and 1.5k only ? Homework EquationsThe Attempt at a Solution How about FR = 4.5k and also the 1k ? Cant i just consider all of them ...
  34. Chadi B Ghaith

    Understanding Absolute Viscosity - shearing stress

    Understanding Absolute Viscosity - shearing stress Hi everyone, I have found information about Absolute viscosity: Coefficient of absolute viscosity is a measure of internal resistance. Dynamic (absolute) viscosity is the tangential force per unit area required to move one horizontal plane...
  35. A

    I Exploring the Connection Between Charles Law and Absolute Zero in Ideal Gases

    Why do all the volume temperature curves of an ideal gas intersect at the same point on the temperature axis ?
  36. M

    B Why is the use of absolute value in vector norms a matter of preference?

    I would like to ask you why the author does not use absolute value of y instead of y? Source: Mathematical Methods in the Physical Sciences by Mary L. Boas Thank you.
  37. P

    Finding Absolute Zero Values from Best Fit Lines with & w/o Uncertainty

    In one of my problems, I have this set of data. I have to create two best fit lines, and find a value of absolute zero for both. The first best fit line is to be made assuming there is NO uncertainty in P. This is rather straightforward, just use the normal linear regression, find a slope...
  38. karush

    MHB Use absolute converge test

    $$\sum_{k=1}^{\infty}\left(\frac{k}{k+1}\right)^{2k}$$ $\textsf{how do you use absolute converge test on this?}$ ☕
  39. Doctor Strange

    I Can Time be Measured Absolutely w/ SNe Ia Near a Black Hole?

    If I take a spaceship and park it near the event horizon of a black hole and then measure the age of the universe by observing SNe Ia, then travel back out to normal space (no gravitational forces, at rest with respect to CMB), will the dates agree? That is, if the measured age of the universe...
  40. Genilson

    I Limit with integral and absolute value

    Hello good evening to all, I was studying here and got stuck with this. I solved the integral and got [x+sin(x) -1] and that´s the farthest that I got. I would appreciate the help.
  41. Battlemage!

    B Absolute convergence Text Book question: Boas 3rd Ed

    In Mary L. Boas' Mathematical Methods in the Physical Science, 3rd ed, on page 17 it goes over absolute convergence, and defines the test for alternating series as follows: An alternating series converges if the absolute value of the terms decreases steadily to zero, that is, if |an+1| ≤ |an|...
  42. emcsquared

    When is gauge pressure absolute pressure?

    Homework Statement Hi Physics gurus, this question was in my Chem Eng exam, and I can't agree with my lecturer's answer. He makes a LOT of mistakes, so it's hard to know when he's being clever or reallllly dumb. The question I have issue with is: "Is the pressure a manometric or an absolute...
  43. R

    Absolute temperature for average translational kinetic energ

    Homework Statement The ammonia molecule (NH3) has a dipole moment of 5.0×10−30C⋅m. Ammonia molecules in the gas phase are placed in a uniform electric field E⃗ with magnitude 1.3×106 N/C . Part A: What is the change in electric potential energy when the dipole moment of a molecule changes...
  44. avito009

    Two ways of detecting absolute motion

    There are two ways by which absolute motion might be detected: by measuring motion with respect to a beam of light, and by making use of inertial effects that arise when an object is accelerated. So why MichelsonMorley experiment showed the first method to be unworkable? Einstein's special...
  45. Jlister

    Absolute Relativity (who needs virtual photons anyhow?)

    I've seen, in the description of a black hole's photon sphere, a mention of a "light-like ds." I was happy to see it because I've been thinking about a photon's physical environment; at the speed of light, it would experience no radial dimension & no time dimension. Might it make more sense to...
  46. R

    I Absolute magnitude in cosmology

    When referring to the absolute magnitude ,for example, in the B filter of a distant galaxy(considered point source) what are we talking about? Are we talking about the observed redshifted flux density(luminosity density) hypothetically seen from 10 pc away (1) ; or are we talking about the...
  47. liluiass

    Prove: |x+y|<|xy+1| for |x|,|y|<1

    Homework Statement X and Y 2 real numbers / |x| <1 and |y|<1 Prove that |x+y|<|xy+1|Homework EquationsThe Attempt at a Solution |x+y|<2 I couldn't prove that |xy+1| >2 And couldn't find a way to solve the problem Please help
  48. N

    Double integral with absolute value

    Homework Statement I am trying to evaluate double integral ∫∫D (|y - x2|)½ D: -1<x<1, 0<y<2 Homework Equations None The Attempt at a Solution I know that in order to integrate with the absolute value I have to split the integral into two parts: y>x^2−−−>√y−x2 y>x^2−−−>√y−x2 I just can't...
  49. Oganesson

    I What happens to Quantum decoherence at Absolute Zero?

    .
  50. D

    B Superposition at absolute zero

    I googled a bit about this and managed to find this http://arxiv.org/abs/quant-ph/0505056 http://physics.bu.edu/~mohanty/physica-decoherence.pdf Since I can't make much out of them, maybe except this interesting phrase in the first one "First of all it is intriguing that even at absolute zero...
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