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. L

    Determining the absolute convergence, convergence, or divergence of a series.

    Homework Statement \Sigma from n=0 to infinity (-10)n/n! Determine the absolute convergence, convergence, or divergence of the series. Homework Equations In this section, it's suggested that we use the following to determine a solution: A series is called absolutely convergent if the series...
  2. L

    Absolute Temperature and the Ideal Gas Law

    Homework Statement A cylinder in a car engine takes Vi = 4.50 x 10^-2 m^3 of air into the chamber at 30°C and at atmospheric pressure. The piston then compresses the air to one-ninth of the original volume (0.111Vi) and to 20.0 times the original pressure (20.0 Pi). What is the new...
  3. E

    Gauge and Absolute Pressure- Hydraulics

    Homework Statement I am reading through my introductory course notes, and am given a question I don't understand how to answer. A rectangular tank contains fresh water inside it to a depth of 0.5m. The tank is 1m long and .7m wide. a) calculate gauge pressure at the bottom of tank b)...
  4. J

    Solving equation containing absolute values

    Homework Statement I have this equation |2x+7| - |6-3x| = 8. The step I did is to replace the || with () and then solve the equation 2x+7-6+3x = 8 X = 7/5 But how do a go about solving for the second solution? With one absolute value I would |2x + 7| = 8 2x + 7 = +-8 2x = -7...
  5. W

    Divergence involving absolute value

    Homework Statement Part of a problems asks us to show that for a general function f(|r1-r2|)=f(R) that Div[f] only with respect to r1 is the same as Div[f] only with respect to R Homework Equations f(|r1-r2|)=f(R) The Attempt at a Solution I'm really unsure where to start, but I...
  6. J

    Understanding Absolute Values.

    Hey Guys! I've frequently come by this forum and have finally joined it in hopes that I could get some more conceptual insight in understanding math. One thing that I have trouble with is absolute values. I understand that: |x|= \sqrt{x^2} .. and how it can be defined given restrictions on...
  7. P

    Limit approaching infinity with absolute function

    Hi guys, I have a little problem with this question: Determine the limit (x approaching infinity) \frac{|9-3x^{2}|}{x-2x^{2}} (Sorry, I'm not sure on how to use the Latex feature) Anyways, I've combed the forum and found a couple of threads that are somewhat related to my problem...
  8. T

    Absolute Convergence: Complex Homework Equations and Solutions

    Homework Statement [PLAIN]http://img225.imageshack.us/img225/7501/complexh.jpg Homework Equations The Attempt at a Solution How do I show this absolutely converges?
  9. Y

    Calculate 73.936 with Absolute Uncertainty

    Homework Statement Perform the calculation and report answer in proper scientific notation with absolute uncertainty 73.936(+ 0.19%) / [(0.00455+ 0.00096) + (0.011889(+0.73%))] Homework Equations Addition/Subtraction: Absolute uncertainty = square root(uncertainty1 + uncertainty2)...
  10. A

    Minimizing Sum of Absolute Values

    Hello all, I am trying to solve a problem based on some computer programming task I am trying to solve, and I have encountered a situation I am having trouble continuing.. Given a function f(x)=|1-x| + |0.5-2x| ... How can I find it's minimum efficiently? This sum may extend to 4 or 5...
  11. J

    Transmission Spectrum- Absolute units?

    Homework Statement In manipulating transmission spectrum data from GaAs and InP I'm told to "Look up the refractive indices of GaAs and InP in the region of  = 1.0 micron, and use these to correct your experimental data for reflective losses and plot the corrected transmission T’ in...
  12. L

    Absolute Zero, about -273.15ºC, is the coldest known temperature

    Absolute Zero, about -273.15ºC, is the coldest known temperature possible, where matter it's self, stops moving, and energy can't build up. But, could there be...say, an absolute ∞? Or like...and Absolute energy? Could these be physically possible, and where would these things be found. What...
  13. K

    I hope that will get you started.

    Homework Statement Prove that, if f is continuous on [a,b] and ∫ab= l f(x) l dx = zero then f(x) = 0 for all x in [a ,b]. Homework Equations Hint- from book- Section 2.4 Exercise 50 Let f and g be continuous at c. Prove that if: (a) f(c) > o, then there exists delta > o such...
  14. M

    Whats the derivative of the absolute value to the power of p?

    Homework Statement Let p>0. What is the derivative of |x|^{p}? Homework Equations The Attempt at a SolutionI know that if p is even, then the derivative is just px^{p-1} . But what if x is odd? Would it turn out to be some piecewise function, such as px^{p-1},\: if x \geq 0 and -px^{p-1}...
  15. A

    Absolute Uncertainty of a Volume

    Determine the absolute uncertainty of the prism's volume. The uncertainty of each measurement is +/- 0.5mm. The length of the prism is 142mm, width is 86mm and the height is 151mm. Thank you!
  16. R

    Absolute error due to reaction time when timing with a stopwatch

    Homework Statement We are given that the reaction time for pressing the stopwatch is 0.2 s (we are measuring 15 swings, t15 = 30.45 s) and we need to determine the absolute error in one swing. The Attempt at a Solution My question here is whether the absolute error for those swings is then 2 x...
  17. S

    I can't understand time dilation in absence of absolute motion.

    According to theory of relativity there is no absolute standard of rest. Now, if Alice and Bob are two observers floating in space, so that Alice thinks that she is at rest and Bob is moving away from her at a speed comparable to that of light and Bob thinks that he is at rest and Alice is...
  18. H

    Series Absolute Convergence Proof

    Homework Statement If \suman2 and \sumbn2 converge show that \sumanbn is absolutely convergent Homework Equations The Attempt at a Solution I think I should do something with the statement 2ab\leq a^2 + b^2
  19. M

    Absolute value of riemann sums

    Homework Statement I'm trying to prove that Sp|f| - sp|f| \leq Spf - spf Where P is a partition of [a,b] and f is function that is riemann integrable. Homework Equations The Attempt at a Solution So I get to a point where M = supf(x) and m = inff(x) then |M|(b-a) - |m|(b-a)...
  20. S

    What is the Mean Absolute Deviation for Daily High Temperatures in St. Louis?

    I understand MAD, but I cannot figure out this question. Here's the information. Daily high temperatures in St. Louis for the last week were as follows: 92, 91, 94, 95, 96, 88,90. The mean absolute deviation based on a 2-day moving average = 3.20 How in the world is it 3.20? I've tried...
  21. D

    Absolute Zero & Speed of Light

    Hi everybody, I would like to begin with apologizing for anything stupid I might say or ask because I am not a qualified physicist. I'd like some minutes of your time because i have a question that's been on my mind far too long and i would really like some help with this. Am I correct when I...
  22. A

    Is time in our universe absolute?

    When it is said that the universe is, for example, 9 billion years old, is it the same everywhere else in the universe? Do the distant quasars that we see know that they are the same age as we figure they are? And what defines the “edge” of our universe. The most distance object that we can...
  23. X

    Absolute Value with a number in front?

    Alright, I'm completely confused. I was given a study guide for my Algebra 2 exam(this isn't homework...) and one of the questions was 2|3x+5| < 16 I've seen the absolute value, but never seen a number in front of it...How do I solve this ?
  24. S

    Exploring Absolute Zero: What Happens When We Reach It?

    i am in the 9nth grade and i am intrigued by the idea of Absolute zero and the phenomenas, my question is what will happen if we reach absolute zero? i know that molecules slow down until they stop, but i don't understand one thing, what is keeping the atoms together, isn't it energy. is there...
  25. S

    Probability of absolute difference

    Homework Statement Let there be m independent samples, each of size n, and are drawn from a population of size N using a design D(S,P). Based on the ith sample i = 1, 2, ..., m, let \hat{\theta_{i}}(s) denote an unbiased estimator of \theta. Let \hat{\theta} =...
  26. R

    Absolute Time Clock Experiments: Einstein's Special Relativity

    Here is my question, starting from a suggested experiment that reminds a known example that Einstein gave about special relativity including a moving train, two mirrors inside the train and a light beam reflected between the mirrors (this suggested thought experiment described here only reminds...
  27. P

    Exploring the Frigid World of Absolute Zero: Boson & Beyond

    i am not exactly sure what happens when the temperature almost reaches absolute zero how things react to this drop and what are boson ( sorry for spelling errors)
  28. S

    Absolute Continuity: Showing f is Increasing on [a,b]

    Homework Statement show that if f is increasing on [a, b], then f is absolutely continuous if and only if for each \epsilon > 0 there is a \delta > 0 such that for each measurable subset E of [a, b], m*(f(E)) < \epsilon if m(E) < \delta. Homework Equations The Attempt at a Solution
  29. G

    Understanding RMS vs. Absolute Value for Calculating Averages in Data Analysis

    I never really understood why using the Root Mean Square of negative data is the preferred method of finding the average of the data as opposed to taking the absolute value of the data and taking the average (arithmetic mean) of that. The example that recently made me wonder about this is...
  30. K

    Finding a Motor with an Absolute Encoder for Angular Position Detection

    Hi all. For a project I am doing, I need to find a motor with an encoder that we can use to detect the exact angular position of the shaft at any given point in time. I'd like to see if there is any motor out there with absolute feedback from the encoder - i.e., that I would be able to read...
  31. A

    What Does Calibration Reveal About Absolute Zero?

    Homework Statement A constant-volume gas thermometer is cal- ibrated in dry ice (which is carbon dioxide in the solid state and has a temperature of −80◦C) and in boiling ethyl alcohol (78◦C). The two pressures are 1 atm and 1.542 atm. What value of absolute zero does the cali- bration...
  32. W

    Find p in R for Absolute Conv. Series: 1/(klog^pk)

    Homework Statement find all values of p in R for which the given series converges absolutely. \displaystyle\sum\limits_{k=2}^{\infty} \frac{1}{klog^pk} Homework Equations Ratio Test Or Root TestThe Attempt at a Solution So I tried using the ratio test and get: \mathop {\lim }\limits_{k \to...
  33. jegues

    Absolute Max Min Problem on Region Bounded by x = \sqrt{1-y^2}, y=x, and y=0

    Homework Statement Find the absolute maximum and the absolute minimum of the function, f(x,y) = x^2 + 2xy - y^2 on the region bounded by, x = \sqrt{1-y^2},y=x \text{ and } y=0 Homework Equations The Attempt at a Solution See figure attached for my attempt. Everything...
  34. J

    Social taboos, religion, ethics, absolute morality, God, etc.

    The below text is not a result of coherent thought. It consists of random pieces. I'm sure you would be able to connect them. If there is absolute religious system, then it's won't too much exaggeration to say that I live in a far too religious atmosphere where almost every individual takes...
  35. jegues

    Another Absolute Maximum Question

    Homework Statement Find the maximum value of the function f(x, y) = x^{2} - y^{2} + x considering only points inside and on the boundary of the region bounded by the curve, x = \sqrt{1-y^{2}}, x=0 Homework Equations The Attempt at a Solution See figure attached for my attempt...
  36. jegues

    What is the Absolute Maximum of a Function on a Bounded Region?

    Homework Statement Find the maximum value of the function f(x, y) = xy(3 − x − 2y) on the triangle R bounded by the positive x- and y-axes and the line x+y = 1. Assume that f(x, y) has no critical points in the interior of R. Homework Equations The Attempt at a Solution See...
  37. A

    Proving Unachievability of Absolute Zero: Uncertainty Principle

    Is the uncertainty principle enough to prove that absolute zero is unachievable? i.e. a particle can't be said to have exactly zero energy, because it can't be said to have exactly any amount of energy.
  38. A

    Find the absolute value of theta 650-theta 420

    Two rays of light of wavelength 650 nm and 420 nm are normally incident on a different grating. If the grating has 5000 slits/cm, what is the angular separation of of the two light rays' second order maximum. -Need to find the absolute value of theta 650-theta 420 I know I need to use...
  39. K

    Using magnets to reach near absolute zero?

    Alright, Could you use magnets to slow matter down enough to reach "near" absolute zero? Heres how it would work. You would have a range of magnets in a chamber, and you would inject the chamber with protons. The magnets are comeing from all directions forcing the proton to stay still. Then...
  40. ╔(σ_σ)╝

    Prove that an even degree poly has either a absolute max or min.

    Homework Statement My brain hasn't been working lately so if you see something weird in my proof pardon me and advice me against it. So the problem states: Show that an even degree polynomial has either an absolute max or min.Homework Equations The Attempt at a Solution Let f(x) be an even...
  41. S

    Kinetic Energy of 3D Fermi Gas at Absolute Zero

    Show that the kinectic energy of a three-dimensional fermi gas of N free electrons at absolute zero is (Mathematica code used) u = 3/5 N Subscript[\[Epsilon], F] Now I know total energy of N particles is this integral u = \!\( \*SubsuperscriptBox[\(\[Integral]\), \(0\)...
  42. R

    Absolute value for a sequence.

    Hey. I have | tn - t | < M How can i show that t - M < tn thanks
  43. K

    Reaching Absolute Zero: Methods to Achieve Superconductors

    I hear how people create superconductors by taking a metal and freezing it to Absolute Zero(0 Kelvin). What are some methods to get this sort of tempuature? Can anyone help?
  44. K

    Are there any absolute moral values for all mankind?

    If so, how did they become absolute to all mankind across cultures and terriotories?
  45. S

    Absolute Max/Min of a Trig Function

    I am having some issues with going about finding the max and min of trig functions over a set interval. Normally with finding the max and min of a function over an interval the first thing that I do is find the derivative of that function, Then i set the derivative to 0 and solve to find the...
  46. A

    Absolute Maximum and Minimum in Calculus: Solving Problems with Graphs

    Homework Statement i did it on paint and print screened to make it more clear what i did :) I am getting, as shown above, 0 for abs max and -15 for absolute min. But it wants -48 for abs min and i have no idea how to get that >:(
  47. P

    Complex number equation - absolute value assumption

    I have a problem in understanding the procedures of a solved example. It goes like this. \left ( \frac{z+i}{z-i} \right )^4 = -1 Therefor we can write: \left | \frac{z+i}{z-i} \right | = 1 From that we can see that z is a real number because: \left | z+i \right | = \left | z-i...
  48. S

    Thermodynamics regarding ideal gases and the absolute zero.

    Hello colleagues, I have a seminar that i need to turn in a weeks day from now. My professor listed the following questions, guidelines that I should lean on: 1) Is it possible to achieve a temperature bellow absolute zero (-273,15) 2) An ideal gas contracts linearly when decreasing...
  49. P

    Equations with multiple absolute value operators

    Hello there. I'm having some problems with absolute values when they contain multiple "abs" operators and some other numbers outside the "abs"-es. For example: \left | x+2 \right | - \left | x \right | > 1 If i check it for the positive scenario, the result is true for all x-es. x+2...
  50. T

    Absolute Extrema of two variables?

    Homework Statement Given function f(x,y) = 3x2 - 2xy + 2y a) find the critical point(s) of f, b) sketch the region R: the triangular region in the xy-plane with vertices (0,0) (0,6) and (3,6) c) find the absolute maximum and absolute minimum of f over R Homework Equations The Attempt at a...
Back
Top