Positive Definition and 987 Threads

Positive liberty is the possession of the capacity to act upon one's free will, as opposed to negative liberty, which is freedom from external restraint on one's actions. A concept of positive liberty may also include freedom from internal constraints.The concepts of structure and agency are central to the concept of positive liberty because in order to be free, a person should be free from inhibitions of the social structure in carrying out their free will. Structurally, classism, sexism, ageism, ableism and racism can inhibit a person's freedom. As positive liberty is primarily concerned with the possession of sociological agency, it is enhanced by the ability of citizens to participate in government and have their voices, interests, and concerns recognized and acted upon.
Isaiah Berlin's essay "Two Concepts of Liberty" (1958) is typically acknowledged as the first to explicitly draw the distinction between positive and negative liberty.

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  1. Telemachus

    I How do I know if a matrix is positive definite?

    Hi. I have a real tridiagonal symmetric matrix that comes from the discretization of a partial differential equation. The elements are given by: ##A_{i,j}=-\delta_{i-1,j}\kappa_{i-1/2,l}\frac{\Delta t}{h^2}+\delta_{i,j}\left[\frac{2}{c}+\frac{\Delta t}{2}\mu_{i,j}+\frac{\Delta...
  2. Math Amateur

    I The Set of Positive Integers - a Copy of the Natural Numbers

    I am reading Ethan D. Bloch's book: The Real Numbers and Real Analysis ... I am currently focused on Chapter 1: Construction of the Real Numbers ... I need help/clarification with an aspect of Theorem 1.3.7 ... Theorem 1.3.7 and the start of the proof reads as follows: n the above proof we...
  3. Math Amateur

    MHB The Set of Positive Integers as a Copy of the Natural Numbers ....

    I am reading Ethan D. Bloch's book: The Real Numbers and Real Analysis ... I am currently focused on Chapter 1: Construction of the Real Numbers ... I need help/clarification with an aspect of Theorem 1.3.7 ... Theorem 1.3.7 and the start of the proof reads as...
  4. lfdahl

    MHB Set of 2015 Consecutive Positive Ints with 15 Primes

    Is there a set of $2015$ consecutive positive integers containing exactly $15$ prime numbers?
  5. T

    Newton's Laws - Positive & negative direction

    Hi, While solving homework problems, I start by defining a positive-y direction and a positive-x direction. Let's say up and to the right. Until now, I've applied this same rule to all objects in each problem, no matter the direction the object moves. But it seems I have not understood this...
  6. Adgorn

    Proving properties of a 2x2 complex positive matrix

    Homework Statement Prove that a 2x2 complex matrix ##A=\begin{bmatrix} a & b \\ c & d\end{bmatrix}## is positive if and only if (i) ##A=A*##. and (ii) ##a, d## and ##\left| A \right| = ad-bc## Homework Equations N/A The Attempt at a Solution I got stuck at the first part. if ##A## is positive...
  7. Adgorn

    Proving the square root of a positive operator is unique

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  8. binbagsss

    Cubic positive solution exists analysis

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  9. psy

    Calculating work done by an Electric field on a positive charge

    Hey How can i calculate the work done by a homogeneous electric field on a positive charge q = 7 × 10^-8 C when the charge moves from point 1 to point 2 . I have two cases: a) the charge is parallel to the Electric field; b) the displacement of the charge takes place at the angle α = 60 ° to...
  10. H

    B Definite integrals with +ve and -ve values

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  11. C

    MHB Proving expression is always positive

    I am trying to prove that $$ x^4+4096y^4+450x^2y^2-2304xy^3-36x^3y $$ is positive for all positive $x$ and $y$. I also have the condition $x>16y$ though I don't believe this is needed to prove positivity as I've plotted the function for varying $x$ and $y$ and it always seems to be positive...
  12. Kuzon

    What is the difference btwn positive and negative electrodes

    I'm so confused, is the voltage reading of the meter gathered by: positive electrode charge - negative electrode charge = potential difference I don't get why there is a positive and negative electrode and what they do
  13. M

    MHB Square Root: Positive & Negative

    Why do we get two answers when taking the square root? For example, let a = any positive number sqrt{a} = - a and a. Why is this the case? What about 0? Can we say sqrt{0} = - 0 and 0?
  14. Mr Davis 97

    Find the values of b for which the roots are positive

    Homework Statement Given that ##f(x) = x^2 - bx + 1##, find the values of b for which at least one of the roots are positive Homework EquationsThe Attempt at a Solution So first I used the quadratic equation to find the roots: ##\displaystyle x = \frac{b \pm \sqrt{b^2 - 4}}{2}##. Now, given...
  15. Albert1

    MHB Is there a solution to $x^2+y^2=1992$ for positive integers $x$ and $y$?

    $x^2+y^2=1992---(A)$ pove $(A)$ has no positive integer solution
  16. M

    Standard addition concentration positive

    I am computing limit of detection of zinc of an electrolyte. Using standard additions method, I have obtained positive x intercepts for 6/8 samples all very close to zero. Positive x-intercepts imply final concentration values to be negative. if x-intercept taken to be zero, the concentration...
  17. Amy

    Flux of high charge positive ions, how?

    I need a flux of highly positive ions, at least penta-valent ions (5+ or more, 6+, 7+, ...); there are ion sources that can generate a proton flux, but I need 5+ ions; do you know how I can do that?
  18. O

    Why Does Amplitude Not Matter in Positive Sequence Detector Circuits?

    Hi, I am studying a positive sequence detector and have some trouble understanding it. I understand most of it, but the author in the book "Instantaneous Power Theory and Applications to Power Conditioning" writes: For extracting the fundamental positive-sequence voltage with the dual method...
  19. M

    B Find the Minimum Value of Expression Involving Positive Real Numbers

    if ## a,b,c,d,e ## are positive real numbers, minimum value of (a+b+c+d+e)( \frac{1}{a} +\frac{1}{b} +\frac{1}{c} +\frac{1}{d} +\frac{1}{e} ) (A) 25 (B) 5 (C) 125 (D) cannot be determined My approach : expanding the expression , i get 5+a( \frac{1}{b} +\frac{1}{c} +\frac{1}{d} +\frac{1}{e}...
  20. F

    Is the Matrix Symmetric Positive Definite for Cholesky Decomposition?

    Homework Statement Here's the question : 1x1+ 2x2 +0x3 + 0x4 = 1 2x1+ 9x2 +1x3 + 0x4 = 6 0x1+ 1x2 +9x3 + 4x4 = 2 0x1+ 0x2 +4x3 + 3x4 = 8 I' m asked to solve this question using Choelsky method ( We need the symmetric positive definite matrix when we are using this method) Homework...
  21. Mr Davis 97

    Is the group of positive rational numbers under * cyclic?

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  22. D

    Double stochastic matrix positive recurrent?

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  23. Adgorn

    B is nonsingular -- prove B(transpose)B is positive definite.

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  24. F

    Why does oxygen carry the positive F.C in [CH3OH2]+?

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  25. TeethWhitener

    I Is a symmetric matrix with positive eigenvalues always real?

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  26. D

    I Prove ln(x) <= x-1 for positive x

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  27. B

    Sound wave -- positive and negative frequency?

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  28. K

    Confusion about work done by friction as negative or positive

    https://lh3.googleusercontent.com/0GOyZeQMdpLgYxYwwP4FMabe-Mk7QpADPC4ZK4PVpBGKvamcqjopOf3M0evdhE8PHZ3iTQ=s138 m1 is 4 kg and m2 is 8 kg. The kinetic friction coefficient on the table is 0.3. m1 is held in place. When m1 is released, m2 accelerates 1.2 m to the floor. Use conservation of...
  29. Albert1

    MHB Prove f(n) is a product of two consecutive positive integers for all n

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  30. A

    Work done in moving a 1C positive charge from one point to another

    Homework Statement Determine the Work done by the electric field E = axX - ay2y in moving a unit positive charge from position p1 (-2,0,0) to position p2 (5,-1,3) the distances are in m Homework EquationsThe Attempt at a Solution I'm not really experienced with forums therefore my attempted...
  31. Ali Hamaiz

    B Is the value of g negative or positive?

    I know that in formus there are many answers about this question .I just want the value of g (will it be positive or negative) in this example which I am going to give , I threw a ball vertically upward the value of g at its max height (vi=0) ,what will be the value of g +10 or -10 m/s^2. I...
  32. Ling Min Hao

    I Positive or negative remainder

    Is 23 = 5(-4)-3 gives a remainder -3 when divided by 5 ? is this statement true ? some of my colleagues said that remainder cannot be negative numbers as definition but I am doubt that can -3 be a remainder too?
  33. R

    Why Is Torque Considered Positive in This Physics Problem?

    Hi, I'm having trouble understanding this attached example in my physics textbook. It notes torque as being positive when substituted back into mg-Ft=-ma rather than being negative which I would think it would be because it is going in the clockwise direction. Can anyone help me understand why...
  34. srfriggen

    B Why is i^2 equal to negative one and not positive one?

    Someone please tell me what is wrong with this logic: i = √-1 i2= √-1√-1 = √(-1)(-1) = √+1 = 1 But also i2 = (√-1)1/2= -1
  35. B

    Proving Least Positive Residue Using m-Cycle Permutations

    Homework Statement Prove that if ##\sigma## is the ##m##-cycle ##(a_1 ~ a_2 ... a_m)##, then for all ##i \in \{1,...,m\}##, ##\sigma^{i}(a_k) = a_{k+i}##, where ##k+i## is replaced by its least positive residue ##\mod m##. Homework EquationsThe Attempt at a Solution My question is...
  36. C

    B States as positive operators of unit trace

    I read that states are positive operators of unit trace - not elements of a vector space. Is it referring to quantum states or all classical states? I know operators are like minus, plus, square root and vectors are like rays in Hilbert space.. but why can't quantum states be vectors when in...
  37. M

    MHB Prove: Positive Integer n Sum Equation

    prove by induction for all positive integers n: 1+5+9+13+...+(4n-3)= n/2(4n-2) i tried this by trying to prove n/2(4n-2)+ (4(k+1)-3) = k+1/2(4(k+1)-2) but it did not work out for me.
  38. M

    Every positive real number has a unique positive n'th root

    Homework Statement Show, using the axiom of completeness of ##\mathbb{R}##, that every positive real number has a unique n'th root that is a positive real number. Or in symbols: ##n \in \mathbb{N_0}, a \in \mathbb{R^{+}} \Rightarrow \exists! x \in \mathbb{R^{+}}: x^n = a## Homework...
  39. kaliprasad

    MHB Lowest Positive $p$: Solving $\cos(p\sin \, x) = \sin (p\cos\, x)$

    find lowest positive p such that $\cos(p\sin \, x) = \sin (p\cos\, x)$
  40. H

    Two equal positive charges are held fixed and separated by d

    Homework Statement Two equal positive charges are held fixed and separated by distance D. Find the electric field vector along their perpendicular bisector. Then find the position relative to their center where the field is a maximum There was another thread with this question but the...
  41. JulienB

    Show that f'(x) grad f(x) is positive

    Homework Statement Hi everybody! I'm preparing a maths exam so I run through a lot of problems, and I am unsure whether I tackled this one correctly or not: Prove that for every differentiable function ##f: \mathbb{R}^3 \to \mathbb{R}## and for every point ##x \in \mathbb{R}^3## the following...
  42. Mr Davis 97

    B Finding the smallest positive solution to trig equation

    I have the equation ##\sin 3x = \cos 7x##, and, in degrees, I have to find the smallest positive solution. Immediately, we can see that sin and cos are equal if their arguments are complements, so ##3x + 7x = 90##, which means that ##x = 9##. I know that that is a correct solution, but how do...
  43. A

    Positive Sequence Resistance and Reactance calculation

    Hi, I have following two parameters with me a) Maximum three phase fault current in amperes (A) and phase angle in degrees (B). I want to calculate the positive sequence resistance (R) and reactance (X) from above two variables for a symmetric system. I couldn't figure out a way to find R and...
  44. Mr Davis 97

    B No distinction between positive and negative for imag nums?

    I am solving for the square root of a complex number, namely: ##\sqrt{5 -12i}## Let's assume for brevity's sake that I already have the solution ##3- 2i##. This is fine and well, but the book that I am reading goes on to say that "##- (3 -2i)## is an equally valid solution, since there is no...
  45. Albert1

    MHB Proving $f(2) \geq 27$ with Positive Coefficients

    given :$f(x)=x^3+ax^2+bx+1$ with $a\geq 0 \,\, and \,\, b\geq 0$ and also all of the three roots of $f(x)=0$ are real numbers, prove $f(2)\geq 27$
  46. akashpandey

    I Why Do Opposite Charges Attract?

    I know its very basic but still. From the school level we thaught that positive attracts negative. But i still don't know what is reason behind it. Why this work on atomic level? What is the reason behind the electrostatic attraction?
  47. giokrutoi

    Finding All Pairs of Positive Integers for (22016+ 5)m + 22015 = 2n + 1

    Homework Statement (22016+ 5)m + 22015 = 2n + 1[/B] find every n and m pairs as they are positive integersThe Attempt at a Solution (22016+ 5)0 + 22015 = 22015 + 1[/B] so one pair is m= 0 , n = 2015 if m =1 the equation is meaningless if m> 1 so there are really amount of powers that...
  48. S

    Can the work of a counterclockwise cycle be positive?

    Consider an ideal gas following a thermodynamics cycle, represented on a ##P-V## plane. I read that if the cycle is "travelled" clockwise then ##W_{gas, cycle}>0## so the gas does positive work, while if the cycle is "travelled" counterclockwise then ##W_{gas, cycle}<0## but it seems to me that...
  49. J

    Can You Solve for the Positive Definite Matrix with Eigenvalues 1 and 2?

    Homework Statement a positive definite matrix has eigenvalues λ=1 and λ=2. find the matrix Homework EquationsThe Attempt at a Solution I've used a 2x2 matrix with entries a0,a1,a2,a3 as the unknown matrix but no use. (As little as i know a0 and a3 should be 1 and 2 respectively...
  50. Mr Davis 97

    B Finding the first 40 positive odd integers

    I have the following problem: What is the sum of the first 40 positive odd integers? I look at the solution, and it says that "The sum of the first 40 positive odd integers is ##1 + 3 + 5 + \dotsm + 77 + 79##. And then it goes on with the solution. My question is, how do I find that 79 is...
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