# 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. ### B I need help understanding the derivation of this 'Absolute Scale of Temperature'

It is from [ Class 11th] SL Arora, pg no. 11.3, the heading is [11.7] Absolute Scale of Temperature.
2. ### I What is “absolute circular polarization fraction” for a pulsar?

In a pulsar paper, two terms were mentioned: circular polarization fraction and absolute circular polarization fraction. 1. What is the absolute circular polarization fraction? 2. What is the difference between them?
3. ### I 3 clocks thought experiment - Absolute vs. relative aspects?

Here are two similar, quite simple thought experiments, followed by assumptions on final clock readings. In the end, my most important question to them. Exp1: - we have two space ships, ss1 and ss2, both have clocks on board, named cl1 and cl2 - we have a third clock, cl3, somewhere located in...
4. ### Why must we use absolute temperature for the Ideal Gas Law?

For this problem, The solution is, However, why must we use absolute temperature for the ideal gas law (i.e why can we not use Celsius for T) Many thanks!
5. ### Trying to understand the property of absolute value inequality

First lets focus on ##|x|## which is defined as distance between ##x##and ##0##. But if we look into it closely $$13=|-11-2|$$ which is distance between -11 and 2 but $$13=|11-(-2)|$$ which means this is distance between 11 and -2. Which is it? In the same way $$x=|x-0|$$ is distance between 0...
6. ### Finding Absolute Uncertainty in Data

For this data, I am trying to find the overall absolute uncertainty of NA, where NA is the numerical aperture: ##\tan \theta_{NA} = \frac{R}{L}## and ##NA = \sin \theta_{NA}## Case R(cm) L(cm) R/L theta_NA[rad] NA error in NA R0,L0 0.5 0.5 1 0.785398163 0.707106781 0 Rmax,Lmax 0.7...
7. ### POTW A Test for Absolute Convergence of a Series

Let ##\{a_n\}_{n = 1}^\infty## be a sequence of real numbers such that for some real number ##p > 1##, ##\frac{a_n}{a_{n+1}} = 1 + \frac{p}{n} + b_n## where ##\sum b_n## converges absolutely. Show that ##\sum a_n## also converges absolutely.
8. ### Concept of Absolute Thermodynamic Activity

In the textbook Electrochemical Systems by Newman and Alyea, Chapter 14: The definition of some thermodynamic functions, chemical potential of component (ionic or neutral) is written as a function of absolute activity: $$\mu_i=RT\ln(\lambda_i)\tag1$$ where ##\lambda_i## is the absolute activity...
9. ### I Absolute value bars in dot product derivation

Dose someone please know why they have the absolute value bars in this derivation? many thanks!
10. ### B Electrons at Absolute Zero -- do they still move?

Can we all agree that electrons still move at absolute zero?
11. ### Using Arduino to Obtain Absolute Orientation from a 6-Axis Gyro

The gyro has 6 inertial axes and 3 magnetic axes. How do I make them work together to get the orientation of the rocket in the reference fixed to the ground? I found something from Matlab but I am not sure how it works...
12. ### Solving an absolute value quadratic inequality

Im a having trouble understanding how this exactly works. $$|x^2 - 4| < |x^2+2|$$ So I know the usual thing to do when you have absolute values,here it is even simpler since the right part of the inequality is always positive so I just have these 2 cases. 1. ## x^2-4 >= 0 ## and 2. ## x^2-4...
13. ### Finding percentage and absolute uncertainties

the answers to other parts of the question: a, 2.0×10-⁷ b, 40 N c, O.O5 d, 4×10⁹Pa I Really don't understand how to solve the e part I Know that Young modulus= (Force÷Area)÷(Extension÷Load) kindly guide how to solve this question.
14. ### B Rotation is absolute, linear motion is relative?

Can you explain with example what mean rotation is absolute and linear motion is relative?
15. ### Quadratic inequalities with absolute values

I was given a problem to solve that goes like this ##\frac{3}{|x+3|-1}\geq |x+2|## . I got the correct solution for all possible cases and here they are; for ##|x+3|\geq0## and ##|x+2|\geq## i got ##x\epsilon <-2, -2\sqrt{3} ]## and for ##|x+3|\leq0## , ##|x+2|\leq0## I got ##x\epsilon [-5...
16. ### Solving an inequality involving absolute values

Problem Statement : I copy and paste the problem as it appeared in the text to the right. Attempt (mine) : I copy and paste my attempt using Autodesk Sketchbook##^{\circledR}## below. I hope the writing is legible. My answer : I have three answers and confused as to which of them hold...

31. ### I Absolute and relative motion/rest

In matter of absolute rest and relative rest as per Newton's laws, one thing that confuses me. If a train or bus is moving for example, if one sets aside for a moment the rotation of the Earth and its orbit around the sun, one could say that the Earth was at rest and that a train on it was...
32. N

### Rewrite an Expression to Eliminate Absolute Value

See attachment. I don't understand the solution given by David Cohen. 1. Note: x^2 is nonnegative for any real number x. This is because any value for x when squared is positive. Yes? 2. If x is greater than or equal to 0, then I can say that -2 - x^2 is negative in value, right? 3. What...
33. N

### Simplify An Expression Containing Absolute Values

See attachment. I don't understand the solution given by David Cohen. I am sure this is a shortcut explanation. I don't like shortcut explanations. 1. What in the problem indicates that x > 1? 2. What in the problem indicates that x < 2?
34. N

### Absolute Value (algebraic version)....2

Absolute Value (algebraic version) Rule: | x | = x when x ≥ 0 | x | = -x when x > 0 Rewrite each expression without using absolute value notation. Question 1 | x^4 + 1 | I say x^4 + 1 is a positive value. My answer is x^4 + 1. Question 2 |-sqrt{3} - sqrt{5} | The value of -sqrt{3} -...
35. N

### Absolute Value (algebraic version)....1

Absolute Value (algebraic version) Rule: | x | = x when x ≥ 0 | x | = -x when x > 0 Rewrite each expression without using absolute value notation. Question 1 |1 - sqrt{2} | + 1 The value 1 - sqrt{2} = a negative value. So, -(1 - sqrt{2}) = - 1 + sqrt{2}. When I put it all together, I get...
36. ### I C in a Vacuum: Evidence of Constant?

I understand that it is one of Einstein's postulates, however I don't know of any direct experiments which show that it is true.
37. ### Who Can Solve the Mystery of the True Torque?

Alright how do I explain this. I am looking for the true and absolute equation of torque, specifically, the ratio of angular acceleration to torque. Basically, I got the equations from online, but then found out from another website that most online equations are bogus, my estimate is 99%. The...
38. ### Classical Looking for the absolute best fluid mechanics book available

Dear physics forum dwellers, Currently on search for an advanced fluid mechanics book that covers all the nitty gritty details. Not looking for general introduction books like Munson, Rothmayer, ... or Cengel that are used in bachelor physics classes or engineering classes. Even after skimming...
39. ### Finding Absolute Minima & Maxima of a Function

Good day, I have a question regrading how to find the absolute minima maxima of a function , I understand that first we need to calculate the Hessian Matrix to find the relative minima /maxim but after we need to check the borders of the region ( a rectangle in our case) for example we put x=-2...
40. ### Need help with Finding absolute magnitude

P is = to 7 and I don't know how to get the absolute magnitude please help.
41. ### Whether a non-inertial frame is absolute

If a frame is a non inertial frame, then it must have an acceleration. Then which reference frame is this acceleration with respect to? If this acceleration varies with the reference frame this acceleration is calculated with respect to, is this non inertial frame absolute?
42. ### Absolute zeros other than temperature (e.g. pressure)

Hi. A version of the third law of thermodynamics states that no system can be cooled down to absolute zero temperature in finitely many steps. But what about other quantities, for example pressure: Is it possible (in principle) to evacuate a system up to the last gas particle, or would this...
43. ### I Is acceleration absolute or relative - follow up

Hello, Some doubt arose me reading this thread https://www.physicsforums.com/threads/is-acceleration-absolute-or-relative-revisited.999420/post-6454462 currently closed. Sorry, I have not be able to quote directly from it :frown: Your claim is not , however, asserting that the spacetime...
44. ### How to Calculate Absolute Gamma Probability from Relative Intensities?

Hi All, I want to ask how to calculate the absolute gamma probability from relative intensities ( found on the tables of nucliedes) following alpha or beta decay. I mean the probabilities that all add to 1. Many thanks.
45. ### Is there such thing as an absolute measurement?

To want to know the exact quantity of an object whether it be it's length, width, weight etc... Doesn't an absolute measurement only exist in the math/our human Minds. Then go down to quantum scales and that gets even harder because from what point do we even measure from if there is no exact...
46. ### B Does Absolute Value Affect Fraction Equality?

Is it correct that ##\frac{|x + 1|}{|x + 2|}## equal to ##\left|\frac{x + 1}{x + 2} \right|##? Please explain, I don't understand. Thank you
47. ### How to represent this absolute value inequality with constants?

see attached image, it asks to repesent it in x-graph constant "a" isn't conditioned. Do I need to separate it into a few cases of the constant a and represent each in one x-graph?
48. ### MHB Absolute value of real numbers

Reals $x,\,y$ and $z$ satisfies $3x+2y+z=1$. For relatively prime positive integers $p$ and $q$, let the maximum of $\dfrac{1}{1+|x|}+\dfrac{1}{1+|y|}+\dfrac{1}{1+|z|}$ be $\dfrac{q}{p}$. Find $p+q$.
49. P

### I Is acceleration absolute or relative - revisited

Hello all, I just joined this group after stumbling over a post from 2003 on this topic. The issue I'd like to deal with is the spinning bucket of water and why the water will still climb up the sides of the bucket if the bucket is stationary. In the original post an Absolutist put it like...
50. ### B Volume of a solid at absolute zero

How much does a typical solid shrink when cooled from room temperature to absolute zero. I can't solve this myself because the coefficient of linear thermal expansion varies with temperature