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.

View More On Wikipedia.org
Recent contents Top users
  1. Mr Davis 97

    B Solving absolute value equation

    I have the following equation: ##\left | r-5 \right | = \left | r+2 \right |##. What is a general, analytical way that I can solve equations like these? I always get stumped when trying to solve them...
  2. A

    Is there any absolute proof that photons exist?

    I mean, look this stupidity: [Mentor's note - link to crackpot site deleted] This guy denies that light photons exist, and that we are 'magically creating it' like cyclops X-Men This is worst than flat-earthers, I wonder If there is some evidence or is it unfalsifiable, like solipsism? Because I...
  3. G

    I Would any physical event happen at absolute zero?

    For example if we could bring a radioactive atom to absolute zero, would it still be subject to the random radioactive decay? Or would absolute zero inhibit the normal half-life decay of the element? Perhaps in other words, would absolute zero inhibit the elapsing of time?
  4. M

    Two dimensional plane equal absolute nothing

    Hi, as we know all objects must be three dimensional. If there is two dimensional "object" or "shape" in the universe, "it" will not look different from space or nothing as "it" is neither thick nor thin. Mathematicians calling "it" as a "surface" but "it" have zero thickness, isn't it a...
  5. Binky

    Classical Absolute Beginner's Guide to Learning Maths & Physics

    For someone (like me) who is fascinated by maths and physics, but has had no education to speak of other than rudimentary basic stuff that was taught in my rather poor comprehensive school, finding a decent way to self teach is a bit daunting. The 'Dummies' books put me off a bit, I bought a...
  6. C

    B How can we tell that "fictitious forces" are not real?

    Earlier today I was reading through this entire thread: https://www.physicsforums.com/threads/implications-of-the-statement-acceleration-is-not-relative.670653/ And I remained confused about one thing in particular. The original poster made a statement (bolded below) on page 1 that seemed...
  7. S

    Determine the absolute maximum bending stress of the beam.

    Homework Statement If w = 74 kN/m , determine the absolute maximum bending stress in the beam in MPa. Homework Equations I'm not too sure how to go about my calculations. Please help! The Attempt at a Solution I = [(1/12)*(200*256^3)] - [(1/12)*(192*250^3)] = 29.62*10^6 F = 74*24*1000? [/B]
  8. A

    B Why Absolute Zero is Independent of Substance Properties

    Why absolute zero of temperature doesn't depend upon properties of substance?
  9. JulienB

    Proving absolute converge with minorant criterion

    Homework Statement Hi everybody! I'm stuck on a problem in which I don't manage to prove absolute convergence (or not) of the series ∑ (-1)j/(√j + √(j+1)). Homework Equations Leibniz criterion, minorant criterion, limit comparison test, maybe others The Attempt at a Solution So first I...
  10. DavidReishi

    I Square of absolute value of amplitude for a single photon

    I understand that this determines a probability, but of what exactly for a single photon? The probability that the photon will be detected on a surface where the photon is pumped, e.g. where on the surface the laser is aimed?
  11. A

    Absolute function into piecewise function

    Homework Statement Write F(x)= x2-5|x| as a piecewise function Homework EquationsThe Attempt at a Solution I was writting it out and came to Fx= x2-5(x) and x2-5(-x) but my book says that it comes out to be x2-5 x2-5(-x) I imagine there is a very simple reason why the x in the first one...
  12. Tollendal

    Negative absolute temperatures

    https://www.mpg.de/research/negative-absolute-temperature A temperature below absolute zero Atoms at negative absolute temperature are the hottest systems in the world January 4, 2013 What is normal to most people in winter has so far been impossible in physics: a minus temperature. On the...
  13. R

    MHB Absolute max/min over intervals

    Hello, I'm doing: Find absolute min/max of f(x)=x^3-12x^2-27x+8 First I found derivative and when I solved, I got x=9 and x=-1. So I have to find max/min for 3 different intervals: a) [-2,0] And I thought absolute max=-1 and absolute min = none? b) [1,10] max= none min= none c) [-2,10]...
  14. J

    Absolute max and min of multivariable function

    Homework Statement f(x,y) = x2-4xy+5y2-8y ; enclosed by the triangular region (0,0), (3,0), and (3,3) Find the absolute maximum and minimum Homework Equations N/A The Attempt at a Solution First I took the partial derivatives with respect to x and y: fx = 2x - 4y fy = -4x + 10y -8 I...
  15. JustDerek

    How do I combine equations for absolute independent motion with pulleys?

    Homework Statement I've been given a problem with pulleys which I have attached to this post. I've derived the equations shown in the post but I'll also write them below. What I'm struggling with is how to combine them. Homework Equations ##l_1=S_a+2S_c## ##l_2=S_d+(S_d-S_c)##...
  16. F

    Find absolute minimum of f(x)=sin(x)-cos(x) on [0,pi]

    Homework Statement Find the absolute minimum of f(x)=sin(x)-cos(x) on [0,pi] Homework Equations - The Attempt at a Solution I know the answer is 0 from looking at a graph, but I cannot figure out how to express my workings algebraically. The end goal of this is to do a presentation on how I...
  17. Steve619

    Understanding Absolute Error in Machine Measurements: The 1.3% Mystery Unveiled

    In writing up on errors and knowing the error of the machine used (as told by the technician) as being 1.3% where I have a table of theoretical and measured values, The absolute error the difference between the theoretical and measured value, but where does the 1.3% error come into play? And...
  18. T

    Gravitational Waves: Speed, Catching Up & Rules

    Could I catch-up to a gravitational wave? Do the same rules apply as with light -- meaning the speed of GRs are frame independent, etc? Thanks.
  19. C

    MHB Proving an absolute value inequality

    If $\left| a \right| \le b$, then $-b\le a\le b$. Let $a,b \in\Bbb{R}$ The definition of the absolute value is $ \left| x \right|= x, x\ge 0$ and $\left| x \right|=-x, x< 0$, where x is some real number. Case I:$a\ge 0$, $\left| a \right|=a>b$ Case II: a<0, $\left| a \right|=-a<b$the solution...
  20. J

    Ideal gas temperature proportional to absolute temperature

    Homework Statement I[/B] have some difficulties proving that the ideal gas temperature is directly proportional to absolute temperature defined by the second law of thermodynamics. Homework Equations The ideal gas temp. is defined by the ideal gas equation: pV=NkTi(T), where k is Boltzmann's...
  21. G

    Understanding Why We Need Absolute Value for x

    Homework Statement why we need to make x as absolute value ? as we can see, the original is x , why we we need to make x as absolute value ? is the working wrong ? Homework EquationsThe Attempt at a Solution
  22. Mr Davis 97

    Absolute value in a differential equation

    Homework Statement ##\displaystyle (x+3)\frac{dy}{dx} = y - 2##, where x is not 3 and y is not 2. Homework EquationsThe Attempt at a Solution ##\displaystyle (x+3)\frac{dy}{dx} = y - 2## ##\displaystyle \frac{dy}{y-2} = \frac{dx}{x+3}## ##\displaystyle \int \frac{dy}{y-2} = \int...
  23. M

    MHB Integration by parts with absolute function

    Hi all, I have the average value of a function between limits of 7.3826 and 0 which equals 0.4453. I have used the formula for average value function and attached the equation I need solving as I don't know how to use the Latex commands. P is what I am trying to work out. Unfortunately I have...
  24. nandodean

    Questions of Absolute Light Speed & Mass by an Engineer

    Hello everybody. I am an spanish student of a bsc in Chemical Engineering, so as you can imagine, all this questions are going to be purely curiosity. First of all, sorry for any english language mistake I can commit. I have always been curious of the spacetime issues, and how the world really...
  25. S

    Absolute compression = true randomness?

    So I've read from various places that maximal compression produces a truly random output. But suppose you were going to apply compression to a truly random series of numbers with something like LZW. Well wouldn't it be the case that since randomness often produces sequences which do not appear...
  26. T

    MHB Proving absolute values theorems

    For all real numbers $x$ and $y$ , if $x + y >= 0$ then $|x + y| = x + y$. How would I prove this? My textbook just assumes this to be true.
  27. Odious Suspect

    When to introduce absolute value in hyperbola expression?

    We begin with this definition of a hyperbola. \left(\overline{F_1 P}-\overline{F_2 P}=2 a\right)\land a>0 Perform a few basic algebraic manipulations. \sqrt{(c+x)^2+y^2}-\sqrt{(x-c)^2+y^2}=2 a \sqrt{(c+x)^2+y^2}=2 a+\sqrt{(x-c)^2+y^2} (c+x)^2+y^2=4 a^2+4 a \sqrt{(x-c)^2+y^2}+(x-c)^2+y^2...
  28. M

    Find Min Surface Area: Absolute Min & Max Homework

    Homework Statement The surface area of a cell in a honeycomb is S = 6hs + (3s2/2)((√3 - cosθ)/sinθ) where h and s are positive constants and θ is the angle at which the upper faces meet the altitude of the cell. Find the angle θ (π/6 ≤ θ ≤ π/2) that minimizes the surface area S. Homework...
  29. C

    Absolute zero should be impossible

    So since heat comes from atoms vibrating and moving and as they go fast heat increases and when they go slower heat decreases. If I got this right absolute zero is when they give off no heat and this would mean that the atoms are not moving at all. Well then if that is how absolute zero works...
  30. C

    I Absolute Heat: Exploring Extreme Temperatures and Safety Risks

    So there is an absolute zero but is there an absolute heat. What I'm thinking is that it would be something like a particle traveling 99.9999...% the speed of light through a plank length. Let's say there is how hot would this be could we even obtain this heat without jeopardizing safety.
  31. O

    MHB Limit of Absolute Values and Metric Spaces

    Let $\lim_{{k}\to{\infty}}d\left({x}_{m\left(k\right)},{x}_{m\left(k\right)-1}\right)=\varepsilon$ and $\lim_{{k}\to{\infty}}d\left({x}_{n\left(k\right)},{x}_{m\left(k\right)}\right)=\varepsilon$...Can we say that...
  32. T

    Pascal - absolute sum of digits

    Homework Statement Make an "absolute sum of digits" of a number in a particular numerical system. You are given two numbers (numerical system and your number N). You take the number N, add up its digits, if the result has more than one digit you add them up again and so on. You end up with...
  33. avito009

    Is absolute pressure same as gauge pressure?

    From what I have read: Gauge Pressure: The amount by which the pressure measured in a fluid exceeds that of the atmosphere. and Absolute pressure: Total pressure at a point in a fluid equaling the sum of the gauge and the atmospheric pressures.So Absolute pressure= Patm+ P-Patm= P (Which is...
  34. L

    Is "now" relative or absolute?

    I would like to know if an infitesimal unit of time is relative or absolute. If a supernova sweeps away the Pillars in the Eagle Nebula, would it be correct to imagine that as I type this the gas/dust is being displaced or otherwise altered at the exact same instant even though images obviously...
  35. Steve Turchin

    Complex absolute value inequality

    Solve the following inequality. Represent your answer graphically: ## |z-1| + |z-5| < 4 ## Homework Equations ## z = a + bi \\ |x+y| \leq |x| + |y| ## Triangle inequality The Attempt at a Solution ## |z-1| + |z-5| < 4 \\ \\ x = z-1 \ \ , \ \ y = z-5 \\ \\ |z-1+z-5| \leq |z-1| + |z-5| \\...
  36. T

    Absolute extrema 2 variable function

    Homework Statement find the absolute extrema of f(x,y) = 2x - 2xy + y^2 in the region in the xy plane bounded by the graphs of y= x^2 and y = 1 The Attempt at a Solution first we find the first partials fx(x,y) = 2 - 2y fy(x,y) = 2y-2x 2-2y = 0 when y = 1 2y - 2x = 0 when y=x in this case...
  37. Mr Davis 97

    Solving Absolute Value Limit: x→2

    Homework Statement Solve: ##\displaystyle \lim_{x\rightarrow 2} \frac{\left | x^2 + 3x + 2 \right |}{x^2 - 4}##. Homework EquationsThe Attempt at a Solution I am trying to solve the following limit: ##\displaystyle \lim_{x\rightarrow 2} \frac{\left | x^2 + 3x + 2 \right |}{x^2 - 4} =...
  38. T

    Absolute extrema function of 2 variables

    Homework Statement I need to find the absolute extrema of the function in the specified region f(x, y) = x^2 + xy R = {(x,y): |x|<=2, |y|<=1}The Attempt at a Solution The first partial derivatives are fx(x,y) = 2x+y and fy(x,y) = x They are both 0 only when x and y are both 0. So...
  39. F

    Using Light as a absolute frame of reference?

    If light travels in a straight line , why can't we use it as absolute frame of reference? This thought experiment is done in the absence of external forces and gravity. One person standing inside a box ,sends a photon parallel to the bottom of the box from one end to another end , whether...
  40. heavystray

    Absolute Zero Gas: Is Motion Possible?

    What happen to gas particles at absolute zero? Is it possible that the particles will still be moving ? Thanks in advance
  41. Nemika

    Can superconductors conduct electricity at absolute zero?

    I've just learned that the conductivity of super conductors increases with decrease in temperature and it becomes infinite at absolute zero. But I thought that all motion ceases at absolute zero. So how can current flow in such conditions? And how can its resistance become zero as some...
  42. moondaaay

    How do I solve absolute value inequalities involving polynomials?

    1. Homework Equations Solving Polynomial Inequalities The Attempt at a Solution Then I used the property of absolute value inequality to get rid of it. But I really don't know if I'm doing the right step. Is this correct? So that I could separate them in two cases and find the...
  43. J

    B Absolute Value Inequalities: Solving for x

    Please help me. What is the next step to get rid of the absolute value? I tried using its property but I don't know if its correct.
  44. Pejeu

    Spaghettification and gravity in theory of relativity?

    Per my layman's understanding, the apparent force of gravity, as explained by the general theory of relativity, is actually the result of rectilinear motion at uniform speed through warped spacetime. 1. If that's the case, what actually causes gravity for objects at rest with respect to the...
  45. astrololo

    Showing that the mean of one number and its absolute val...

    Homework Statement I must prove that the mean of one number and its absolute value is superior or equal to 0 but inferior or equal to the absolute value of the number Homework Equations I must prove this by the method of case. The Attempt at a Solution I know that the first case is : x>=0...
  46. Jimbob999

    Absolute Visual Magnitude of Stars

    Homework Statement The Sun has an absolute visual magnitude of about 4.8 and a particular star has an absolute visual magnitude of –0.29. How many times more luminous is this star than the Sun, assuming these stars have similar spectral types and hence colours? a) 100 times b) 125 times c) 150...
  47. C

    Help with structural formula and absolute configuration

    1. Complete structural formula, identify the absolute configuration of each asymmetric center (if it applies) Bond rotation may be necessary2. Is the first one right? The second one which is Newman must be turned to boat and then I write it in the boat?The Attempt at a Solution : On the paper[/B]
  48. R

    Absolute uncertainty of calculated density

    Homework Statement An experiment to measure density, d, of a cylindrical object uses the equation d=m/(pir^2l) where m=mass=0.029 +-.005kg r=radius=8.2 +-.1mm l-length=15.4+- .1 What is the absolute uncertainty of the calculated value of the density? Homework Equations above The Attempt...
  49. J

    How can the absolute value of x be negative?

    Homework Statement http://imgur.com/RlIdmFh http://imgur.com/3dnLK3m Homework Equations |x| = -x? The Attempt at a Solution I'm trying to make sense of this definition in my book because they are trying to prove the triangle inequality(second link), yet it keeps saying that the absolute value...
  50. Fancypen

    What are the rules to know when to use absolute value?

    Specifically when doing integration problems. I know the indef integral of cosx/sinx+1 is ln(sinx+1) + C, but absvalue is not required here. I think it's because the sine fn must be >= 0 or it's undefined? What about in other cases, is there a general rule to know when to use absvalue? Thanks
Back
Top