What is Positive: Definition and 983 Discussions

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. M

    Can an interval with all positive functions of x be proven?

    Can an interval with all positive functions of x be proven?? f(x) has to always be greater that 0. How do you prove this?? f is continuous as c and f(c)>0. prove that there is an open interval (a.b) centered at c such that f(x)>0 for all x that are elements of (a,b)
  2. F

    Spring question, how do I know it is negative or positive?

    Homework Statement http://img33.imageshack.us/img33/8751/49753333t.jpg Problem #2 [PLAIN][PLAIN]http://img121.imageshack.us/img121/5574/35712633.jpg My question is, why do they take positive x0? Shouldn't it be negative since it is that amount of x displacement away from the spring?
  3. F

    The conservation of energy, why does it work? Negative work vs positive work

    Homework Statement This is the conservation of energy in the absence of external forces ΔKE + ΔPE + ΔTE + ΔU= 0 TE is friction, U is other internal energy, like the spring So expand and disregard U and TE for a moment ½m(v² - v₀²) + mg(h - h₀) = 0 Now comes the...
  4. K

    Proving Isomorphism of R^x/<-1> and Positive Real Numbers

    Homework Statement Show that R^x/<-1> is isomorphic to the group of positive real numbers under multiplication. Homework Equations The Attempt at a Solution I know I need to show we have a homomorphism, and is one - to one and onto in order to be isomorphic. I know all...
  5. M

    Proving a positive series converges

    Homework Statement Let {an}n≥1 and {bn}n≥1 be strictly positive series. If the limit n-> infinity (an/bn) = c /= 0, then the \sum an converges iff \sum bn converges, n≥1 Homework Equations The Attempt at a Solution Since we know that lim (an/bn) = c, then for all ε>0...
  6. F

    Why is angular acceleration positive even though it is going clockwise?

    Homework Statement Go to http://apcentral.collegeboard.com/apc/public/repository/ap08_physics_c_mech_frq.pdf Question two The solution is http://www.collegeboard.com/prod_downloads/ap/students/physics/ap08_physics_c_mech_sgs_rev.pdfThe Attempt at a Solution My question is part d) in the...
  7. L

    Why do positive and negative charges attract each other?

    why do positive and negative charges attract each other?
  8. Y

    Integral Solutions for n,m Positive Integers

    Homework Statement \int ^b_0 cos(\frac{(n-m)\pi}{b}x) dx \int ^b_0 cos(\frac{(n+m)\pi}{b}x) dx n and m are positive integers. The Attempt at a Solution \int ^b_0 cos(\frac{(n-m)\pi}{b}x) dx = \frac{b\;sin[(n-m)\pi]}{(n-m)\pi} Obviously answer is zero if n not equal to...
  9. A

    What makes a matrix positive ?

    Homework Statement Find an example with 2 * 2 matrices for which: 0 (= or < ) a (= or < ) b does not imply a 2 (= or <) b2. the trace and the determinant of both a and b matrices should be positive ! Homework Equations The Attempt at a Solution i just need to know 2 things : 1- is there...
  10. M

    Proving 12 - 22 + 32 - 42 + ... + (-1)n+1)n2 for Every Positive Integer n

    Homework Statement This is a proof problem in the mathematical induction section of my textbook. I am having trouble with question (c). Result: 12 + 22 + 32 + ... + n2 = n(n+1)(2n+1)/6 for every positive integer n. (a) Use the result to determine the formula for 22 + 42 + 62 + ... + (2n)2 for...
  11. P

    Why Don't Electrons Leave Metal When Connected to Positive Terminal?

    I can't understand this and i would be appreciate if somebody help me. If in the metal we have a very big number of free electrons they should go to the positive therminal of the batery even if the other end of the wire is not conected to the negative therminal.What stops them.The copper wire...
  12. L

    Can a non-symmetric matrix be positive definite?

    Let A be a real nxn matrix. What are the requirements of A for A+AT to be positive definite? Is there a condition on eigenvalues of A, so that A+AT is positive definite? Also I am not sure about the definition of a positive definite matrix. In some places it is written that the matrix must be...
  13. T

    Lagrange Multipliers Find 3 positive numbers?

    Homework Statement Find 3 positive numbers x, y and z for which: their sum is 24 and which maximizes the product: P = x2y3z. Find the maximum product. The Attempt at a Solution Ok, I know how to set up the equations. x + y + z = 24 Delta(F) <2xy3z, 2x2y2z, x2y3> fx = 2xy3z...
  14. W

    Proving Existence of Positive Integer Multiple with 0s & 1s

    Homework Statement Let k be any positive integer. Prove that there exists a positive integer multiple n of k such that the only digits in n are 0s and 1s. (Use the pigeonhole principle.) Homework Equations The General Pigeonhole Principle If more than mk things are distributed into k...
  15. T

    How many coulombs of positive charge are in 1.91 mol of O2 gas?

    Homework Statement How many coulombs of positive charge are in 1.91 mol of O2 gas? Homework Equations 1 mol = 6.022x10^23 protons q=Ne The Attempt at a Solution so 1.91 mols x 6.022x10^23 = 1.1502x10^24 protons I divided that by 6.25x10^18 protons in one coulomb, but I got...
  16. D

    If A(x,y) is a Positive Definate Bilinear Form then sqrt(A(x,x)) defines a norm

    Homework Statement The Problem is from Mendelson Topology. Let V be a vector field with the real numbers as scalars. He defines a bilinear form as a function A:V x V -> R s.t for all x,y,z an element of V and real numbers a,b,c A(ax +by, z) = aA(x,z) + bA(y,z) and A(x,by + cz) = bA(x,y) +...
  17. F

    Does the Earth Have an Excess of Positive Charge?

    most of the cosmic rays that hit the Earth is made up of positively charged particles, like protons. This suggests that the Earth has a growing excess of positive charge ... Is this true?
  18. F

    Construct a field with all positive intergers.

    Homework Statement Is it possible to construct a field, that satisfies all basic propeties (http://en.wikipedia.org/wiki/Field_%28mathematics%29#Definition_and_illustration , the six bolded part ), with only and all positive integers? Remeber, you don't have 0/negative numbers/fraction in...
  19. K

    Positive Electricity: Uses, Differences, Repulsion

    Can electricity be positive instead of negative? What differences would it be? Can electricity be used to repel things?
  20. I

    Semi-Positive Definiteness of Product of Symmetric Matrices

    Here is my problem. Any ideas are appreciated. Let P be a projection matrix (symmetric, idempotent, positive semidefinite with 0 or 1 eigenvalues). For example, P = X*inv(X'*X)*X' where X is a regressor matrix in a least square problem. Let A be a symmetric real matrix with only integer...
  21. T

    Is Pushing Against a Car's Motion Positive Work?

    Homework Statement A car is rolling to the right and you try to slow it down by pushing on it to the left. You are doing A) positive work B) negative work C) no work until the car comes to a stop D) You can’t tell because I didn’t tell you which way was positive. Homework Equations...
  22. O

    In what direction does the sphere move between two positive charges

    Homework Statement http://www.screencast.com/users/trinhn812/folders/Jing/media/8fe997e1-46e5-4033-a246-fbad0acb7162 Homework Equations The Attempt at a Solution I understand that in question 25, the conductor becomes polarized and its negative charges will be more attracted...
  23. Z

    Square an inequality if both sides are positive

    I know that we can square an inequality if both sides are positive. But can we cube an inequality provided both the sides are positive? If no then why?
  24. G

    Electric Potential of 2 positive charges, and the speed

    QUESTION 1 Homework Statement Two positive charges, each with Q = +10 µC, are fixed to the x-axis at x = +a and x = -a, where a = 4 m. (a) Find the electric potential at point A on the y-axis where (xA, yA) = (0, b) and b = 5 m. Take the zero of potential to be at infinity. (b) A...
  25. P

    Neither positive nor negative ?

    If we require that the north is positive number,For example +10Km,South for the negative number,For example -10Km,So, what is the number of 10 km east then? I think there are other neither positive nor negative，Not only 0 is neither positive nor negative . Therefore, a number of absolute...
  26. J

    Least positive rest in division?

    Homework Statement Find the least positive rest in division of 7^35 with 5 Homework Equations (7^35)/5 The Attempt at a Solution 7^35=378818692265664781682717625943 => 378818692265664781682717625943/5... Uhhhhh this is not the way I am supposed to take right? :cry:
  27. pellman

    Signicance of positive and negative frequencies?

    Reading some QFT in which we are faced with inhomogeneous equation (\partial^\mu \partial_\mu + m^2)\phi(x)=J(x) The solution is given as \phi(x)=\phi^{(+)}_{in}(x)+\phi^{(-)}_{out}(x)+i\int{d^4 x\Delta(x-x')J(x') where \Delta is the appropriate Green's function. "in" means the...
  28. C

    Entropy of a product of positive numbers

    I accept that the entropy (Shannon's) of a sum of positive numbers is the sum of the -P_n * LOG(P_n) for each number in the sum of numbers where P_n is the average contribution of a term. IE, if T = A + B, then S = -(A/T)*LOG(A/T) - (B/T)*LOG(B/T). But what about the entropy of A*B...
  29. L

    Projectile Motion: two positive times?

    I explained to my class that in projectile motion one always chooses the positive time answer with the negative time answer being dropped. Then a student asked if two positive time answers were possible. I just looked at it assuming that t+/- are both positive and got the result that for t+ to...
  30. S

    Proving Boundedness of a Subset of E with Positive Outer Measure

    Homework Statement Show that if a set E has positive outer measure, then there is a bounded subset of E that also has positive outer measure Homework Equations We can take an intersection of E with some of its covering sets. This will give us a subset of E, but how can we be sure...
  31. S

    Summing Positive Integers with 2^r3^s

    Show that every positive integer is a sum of one or more numbers of the form 2^r3^s, where r and s are nonnegative integers and no summand divides another. not my doubt just found it interesting so posted here :smile:
  32. A

    Positive derivative and strictly increasing

    Isn't it true that if a function f(t) satisfies f'(t) > 0 on some interval, then f is STRICTLY increasing on that interval; i.e., that s < t implies that f(s) < f(t)?
  33. M

    Is the positive terminal of a battery positively charged

    Hi If you are kind enough to answer this please bear in mind that I know next to no physics and I'm quite intimidated by the subject so please don't give me an intractable answer that I won't understand. Please feel free to answer as if you are talking to a nice but dim high school student...
  34. M

    Hamiltonians, do they need to be positive definite?

    Hi (I'm not sure where this question belongs) I had a general question about hamiltonians, do they need to be positive definite? is this required in QM, or is this a relativistic requirement? cheers M
  35. Z

    Does the following inequality holds for every POSITIVE 'x' ?

    does the following inequality holds for every POSITIVE 'x' ? e^{-x}-1\le Cx^{1/4+e} here 'C' and e are positive constants i think that for very very small 'e' the constant must be very BIG but no other hint i find
  36. A

    Work done in moving a unit positive charge in space by an external force

    Consider a positive charge +q placed at the origin. Let A and b be two points in the space with position vectors rA and rB respectively. What will be the work done by an external force equal and opposite to the Coulumbic force, in moving a unit positive charge from A to B, irrespctive of the...
  37. B

    Proving Only 2 Positive Integer Solutions for x3 = y2 – 15

    A problem asks to find all possible pairs (x, y) of positive integers that satisfy the equation: x3 = y2 – 15 There are 2 pairs (so far) that satisfy the equation: x = 1, y = 4 x = 109, y = 1138 It's possible that these 2 points are the only two positive integer solutions...
  38. R

    Room temperature positive magnetoresistance

    I've achieved positive magnetoresistance (MR) in CNT composite thin films with a small percentage of Fe in it. Fe injects spin polarized electrons into CNT. But +ve MR means that resistance is increasing with magnetic field. But due to injection of spin polarized electrons the current has to...
  39. M

    How much energy is need to place four positive charges

    Homework Statement How much energy is need to place four positive charges, each of magnitude +5.0 mC, at the vertices of a square of side 2.5 cm? Homework Equations E = kQ/r^2 The Attempt at a Solution I'm really not sure if what I did is close to correct, but I got an answer...
  40. Z

    trace(A*A) is always positive?

    I have a feeling that for any n x n non-trivial matrix A, trace(A*A) is always positive. Is it true?
  41. D

    Number of ways of expressing n as positive integers

    sorry for the many threads Let S_n denote the number of ways of expressing n as positive integrs.. S_1=1 , s_2=2, s_3=4 .. Prove that S_n=S_{n-1}+S_{n-2} ---S_1+1 no idea to prove that :
  42. J

    Absence of an electron at a point creates a positive charge

    I can't understand how does the absence of an electron at a point creates a positive charge there. In my opinion, it is wrong on account of conservation of charge. Because if we consider an electron(at a point A) as a system, and if the electron get displaced to another point B(in the system)...
  43. H

    Positive definite operator/matrix question

    Homework Statement Prove that T is positive definite if and only if \sum_{i,j} A_{ij}a_{j}\bar{a_{i}} > 0 for any non-zero tuple (a1, ...... , an ) Let A be [ T ]_{\beta} where \beta is an orthogonal basis for T The Attempt at a Solution the sum looked like the matrix...
  44. M

    What is the Minimum Value of f(x) for Positive Real Numbers x and y?

    For all positive real numbers x,y prove that: \frac{1}{1+\sqrt{x}}+\frac{1}{1+\sqrt{y}} \geq \frac{2\sqrt{2}}{1+\sqrt{2}}
  45. D

    Number of positive integers that are not divisible by 17

    Find the number of positive integers in the range of 1976 through 3776 that are not divisible by 17. A={\mathbb{Z}^+\ \mbox{not divisible by 17}} Then I am looking for A^c I am not sure how to do this though.
  46. A

    How can we prove that spring constant is always positive?

    How can we prove that spring constant is always positive??
  47. J

    Simplify and express with positive indices

    Ok, so I have this Expression, (6x+2 x 42x-4 x 35-x x 2x-6)/(124x+3 x 92x-3) But it needs to be simplifyed, and expressed with positive indices. Now as far as my knowledge takes me, this can't be simplifyed, but then I am probably wrong. If anybody could help to solve, that would be great.
  48. J

    Simplify and express with positive indices, a little help?

    Simplify and express with positive indices, a little help? I am no good at these, can anyone show me how to work these out? (18x3 X 2x-4)/(4x-5 X 6x) 83sqrt(p12 q-8) X 34sqrt(p-10 q9) and (6x+2 X 42x-4 X 35-x X 2x-6)/(124x+3 X 92x-3) ps. The Capital X's are multiplication signs
  49. S

    Exploring possibilities of positive foil for stripping electrons

    Hello, I'm thinking of some alternative ways of accelerating particles. I know that it's quite common to have accelerated particles pass along a positively charged foil which strips the electrons of the particles and reverses the particle's polarity. Is there a way to do the opposite? I.e...
  50. S

    Mathematica Taking only the positive sqrt in Mathematica

    As my title says, I need to take only the positive square root of some evaluation. For my calculation, the negative square root is extraneous. What I do is a normalization of a wave function: J = Integrate[Psi[x]^2, {x, 0, a}] sol = Solve[J == 1, A] A /. sol My only problem is those...
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