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. A

    Will batteries' terminal get discharged if the positive one is connected to

    Will a batteries get discharged if the positive one is connected to the negative Hi,yestrday i was told when a wire is connected between two bodies being charged oppositely 'and equally in magnitude' then a sudden discharge take place making the bodies uncharged.So what about the charged...
  2. 2

    Kite string force, negative or positive>

    Homework Statement A kite string exerts a 12-lb pull (|F|) on a kite and makes a 45 degree angle with the horizontal. Find the horizontal and vertical components of F. Homework Equations Pythagorean The Attempt at a Solution 12*sqrt(2) for both horizontal and negative My question is...
  3. N

    Condition on minors to be Positive Semidefinite (PSD)

    Hi everyone, I know that for a hermitian matrix to be PSD it is necessary that every principal minor [i.e, the minors obtained by deleting all the last i rows and columns for all i=(n-1)(-1)0]. I want to know if it is necessary that all minors of order>=2 be non-negative. Particularly, for...
  4. S

    Normal, self-adjoint and positive definite operators

    I have two questions: 1. Let V be a finite dimensional inner product space. Show that if U: V--->V is self-adjoint and T: V---->V is positive definite, then UT and TU are diagonalizable operators with only real eigenvalues. 2. Suppose T and U are normal operators on a finite dimensional...
  5. T

    Limit of f(x) as it approaches from the positive side

    i. Write out the proper definition for lim f(x) x\rightarrowa+ ii. Let g(x)=x-1cos(x-1) Show that for every N and any b>0 there is a point t E (0,6) so that g(t)>N iii. Prove that for g as in (ii) we don not have lim g(x) x\rightarrow0+ I'm not sure what how to do...
  6. A

    Building positive roots from simple roots

    Hi, I've got two related questions. You can decompose a (semisimple) lie algebra into root spaces, each of which are 1-dimensional. If X has root a and Y has root b then [X,Y] has root a+b. If the root space of a+b is not zero (i.e. there is a root a+b) then is it possible for [X,Y] to still...
  7. J

    Maybe stupid question - zero positive or negative ?

    Homework Statement Hi I have to say true or false, and then demonstrate my answer "if taking any 3 Real numbers (a, b, c), we have at least 2 of the same sign" For me its true, i was thinking of creating a triplet (x, y, z), where x=1 if "a" positive, x=0 if "a" negative, same for y...
  8. K

    Summed exponents for a 8- digit positive decimal integer

    ABCDEFGF is an 8-digit positive decimal integer, where each letter represents a different decimal digit from 0 to 9. The digits 1 and 9 do not appear. The nonzero even digits appear in ascending order, and the odd digits appear in descending order in ABCDEFGF. None of A and E can be zero...
  9. K

    Some Summed Digits In A 9-Digit Positive Integer

    Determine a 9-digit positive integer that uses each of the decimal digits from 1 to 9 exactly once, such that: (i) The sum of the digits 1 and 2 and all the digits between them is 9. (ii) The sum of the digits 2 and 3 and all the digits between them is 20. (iii) The sum of the digits 3...
  10. S

    Making negative refraction with positive index material

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  11. R

    Proving Positive Roots of a Cubic Equation: 0<3ab<=1 & b>= 3^0.5

    Homework Statement Suppose 'a' and 'b' are real numbers such that the roots of the cubic equation ax^3-x^2+bx-1=0 are all positive real numbers. Prove that: i) 0<3ab<=1 ii) b>= 3^0.5 Homework Equations Let x,y,z be the roots: x+y+z=1/a xy+yz+zx=b/a xyz=1/a The Attempt at a...
  12. T

    Positive real numbers question

    question: let x_1,...,x_n positive real numbers. prove that \lim_{p\to \infty}\left(\frac{x_1^p+...+x_n^p}{n}\right)^{1/p}=max\{x_1,...,x_n\} can you give me some hints ?
  13. M

    Proving that a^2-2b^2-4c^2 = 0 has no positive integer solutions

    so I have to prove that a^3-2b^3-4c^3 = 0 has no positive integer solutions. I have gotten through most of the proof but now I am stuck, and if you guys could give me a nudge in the right direction that would be great. work done so far: proof by contradiction, i assumed that...
  14. T

    Solving for the Largest Positive Integer n

    Homework Statement Find the largest positive integer n such that n^3 + 100 is divisible by n + 10. Homework Equations The Attempt at a Solution The hint I've been given is to use (mod n + 10) to get rid of the n. but i don't quite see how it would work :S all my attempts...
  15. I

    The difference btn positive and negative potential quantum well

    Homework Statement (a) Determine the reflectivity spectrum R(E) of a free particle of mass m reflected from an infinite jump V(x), where V(x)=0 if x\leq0, V(x)=-\infty if x>0 The other similar problem is: (b) Determine the energy levels of a particle of mass m confined to an infinite...
  16. H

    Is the acceleration due to gravity positive or negative

    I know that purely the acceleration due to gravity is positive because it accelerates things not decelerates or negative acceleration. But in some cases it can be negative but I'm not sure in which cases. For example if I'm just standing here on the ground is gravity working in a positive or...
  17. S

    Find Unit Vector Orthogonal to a & b - Help Needed

    hi! I'm new to the forums, and had a question that was more calculus-related than physics. i saw another post similar to this one, but it was incomplete and i couldn't get the answer with the information on it, any chance someone could help me out? The question is: "Find a unit vector with a...
  18. J

    Simplify and leave in positive exponent.

    Homework Statement (3xy^3)(4x^-3y^-2) Homework Equations ? The Attempt at a Solution = 12y ----- x^2
  19. G

    Point charge attractioning a positive charge from infinity to 30cm

    Homework Statement A point charge of 2.0 10-9 C is located at the origin. How much work is required to bring a positive charge of 4.0 10-9 C from infinity to the location x = 30.0 cm? and it requests the answer in J Homework Equations W=-q2(delta)V DeltaV = Ke q1/d where...
  20. S

    Can an object have a positive velocity and a negative displacement?

    Homework Statement can an object have a positive velocity and a negative displacement? can an object have a negative velocity and a displacement of zero? can an object have a value for distance and an average speed of zero? PLEASE EXPLAIN EACH CASE TO ME! PLEASE LOL :P Homework...
  21. R

    Exchange matrix and positive definiteness

    Homework Statement Let E be the exchange matrix (ones on the anti-diagonal, zeroes elsewhere). Suppose A is symmetric and positive definite. Show that B = EAE is positive definite. Homework Equations The Attempt at a Solution I've tried showing directly that for any conformable vector h...
  22. D

    Prove/Disprove: AB-A^2 is Positive Definite

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  23. K

    Is K Always Positive? Investigating the Positivity of a Quadratic Equation

    Homework Statement This is the equation where i, a, b and c are positive integer. http://www.icedsolo.com/eq.GIF Homework Equations http://www.icedsolo.com/eq.GIF The Attempt at a Solution The question is, proof whether K is always positive, or it is positive in certain range of a, b, and...
  24. A

    What is a positive definite Hamiltonian?

    Can anybody explain what is meant by positive definite Hamiltonian? All I know is that if a Hamiltonian can be factorized as H={Q}^{\dagger}Q then that Hamiltonian is one such example. But I am not sure if that is the definition of a positive definite Hamiltonian. In the quantum mechanical...
  25. A

    Exploring the Differences: Positive & Negative Plots

    Homework Statement I took 2 plots. Can someone explain to me why the first one comes out positive and second negative? Homework Equations The Attempt at a Solution
  26. E

    Lots of positive exponentials leading to huge exponents

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  27. F

    Proving Multiplicative Group of Positive Rationals Generated by Primes

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  28. F

    Can Real Positive Mappings Exceed a Quadratic Function of Their Inputs?

    Homework Statement Prove that for any f:\mathbb{R}\rightarrow\left(0,\infty \right) there is a rational number q and an irrational number i such that f(q)f(i) > \left( \frac{q-i}{2} \right)^2 (Or if this is false find a counterexample) Homework Equations The Attempt at a Solution...
  29. L

    Linear Algebra: Positive Operators

    Homework Statement Let A and B be nxn positive self-adjoint matrices such that for all x \in Cn, x*Ax = x*Bx. Prove that A = B. Equivalently, prove that if A, B are positive operators on H such that <Ax,x> = <Bx,x> \forall x \in H, then A = B. Hint: See Lemma 2.12. Homework Equations...
  30. L

    Linear Algebra: Positive Matrix

    Homework Statement Let T be a positive operator on a Hilbert space H. Pick an orthonormal basis {e1,e2,...,en} for H. Let A=[aij] be the nxn matrix representation of T with respect to the basis {e1,e2,...,en}, so that Tej=\sumaijei, j=1,2,...,n. (The summation is from i=1 to n; I'm not...
  31. G

    Understanding Modulus: Positive, Negative, and the Result

    hi all, i was studying modulus when i came across this mod(xy) = modx mod y we consider 3 cases whereby both positive , both negative, or positive negative it reads here if we consider x and y to be negative it will be something like this mod xy = xy = - mod x ( - mod y ) = mod x mod...
  32. A

    The very significant and positive result of the MM Exp

    The following two main principles are the very significant and positive result of the Michelson-Morley Experiment: 1. The laws by which the states of physical systems undergo changes are not affected, whether these changes of states are referred to the one or the other of two systems of...
  33. R

    Positive Curvature: Maximum Area of Equilateral Triangle

    what's the maximum area of an equilateral triangle that can be drawn on a positive curvature?
  34. C

    Can Acceleration be Both Positive and Negative Simultaneously?

    given acceleration a = 1 + ln x i can find that \Delta v^2 = 2xlnx and since it is given that when t = 0, x = 1,v = 0 \therefore v^2 = 2xlnx however i have been asked to prove v > 0 \; when \;t > 0 and i have no idea how to explain it in mathematcial terms, can anyone please give any suggestion?
  35. P

    Can You Solve This Math Riddle Involving Positive Numbers?

    The difference between two positive numbers is 3. The difference between their reciprocals is 1/90 What are the two numbers? I worked out that: x-y=3 and 1/x-1/y= 1/90 Is that right so far?
  36. N

    Does the Compact Set K+K Have Nonempty Interior?

    Let K\subseteq\mathbb R is a compact set of positive Lebesque measure. Prove that the set K+K=\{a+b\,|\,a,b\in K\} has nonempty interior.
  37. D

    Positive Operator: Why Is \sqrt{A^*A} Positive?

    Given a linear operator A, why is \sqrt{A^*A} positive? Where A* is the adjoint.
  38. N

    Finding a Real Solution for a Complex Equation

    Homework Statement I need to find a positive REAL value x such that \frac{2-(4+x^2-x\sqrt (4+x^2) \sqrt (\frac{2+x^2+x\sqrt 4+x^2 }{8+2x^2})}{4\sqrt (4+x^2) } == 0 x cannot be complex or zero! So far, I don't even think its possible. Any suggestions? Homework Equations The Attempt at a...
  39. A

    Positive Focal Length Image - Real, Diminished, Inverted and Smaller?

    This is a simple wording confusion. On one question that I did, the property for a positive focal length image was Real, Diminished and Inverted. On another question of the same type, the property for a positive focal length image was Real, Inverted and Smaller. So, my confusion is the...
  40. A

    Are All Eigenvalues of a Matrix Between Defined Limits?

    [SOLVED] Positive Definite Matrices Homework Statement a) If A is Symmetric show that A-λI is positive definite if and only if all eigenvalues of A are >λ, and A-λI is negative definite if and only if all eigenvalues of A are <λ. b) Use this result to show that all the eigenvalues of...
  41. A

    Positive Definite Matrices eigenvalues

    [SOLVED] Positive Definite Matrices a) If A is Symmetric show that A-λI is positive definite if and only if all eigenvalues of A are >λ, and A-λI is negative definite if and only if all eigenvalues of A are <λ. b) Use this result to show that all the eigenvalues of [ 5 2 -1 0] [ 2 5 0...
  42. K

    Common multiple of positive integers

    Just have this question I am having trouble with The least common multiple of positive integers a, b, c and d is equal to a + b + c + d. Prove that abcd is divisible by at least one of 3 and 5. Thanks
  43. S

    Is a Career in Physics Worth the Risk?

    Lot of people are telling negative sides career as a physicist, But it physics really in such a bad position? I had a wish to research on high energy physics(particle) . Now i am undergraduate student student of physics major. Should i change field at graduate study? or take risk? If i change...
  44. quasar987

    A limit positive integer and real number

    [SOLVED] A limit Homework Statement How do you show that \lim_{x\rightarrow a}\frac{e^{-a^2/(a^2-x^2)}}{(a^2-x^2)^{2m}(x-a)}=0 for 'm' a positive integer and 'a' a real number >0??This is a type 0/0 indeterminate form but l'Hospital's rule is not helpful because when you differentiate the...
  45. C

    Proving Existence of Integer y and z for x in Positive Integers

    Homework Statement Prove that for all x there exists and x if it is an element of the positive integers, then there is an integer y and an integer z. Homework Equations The Attempt at a Solution I know that the contrapositive would be "If there is not an element of the positive...
  46. D

    Finding Velocity of Positive ion with Volts given.

    Homework Statement An ion is accelerated through potential diff. of 250 V, directly perpendicular to mag. field. Find radius of the path of the ion in the field. Given: mass (m)=2.5 x 10^-26 charge(q)= 1.6 x 10^-19 Volts= 250 V Mag. Field (B) = 0.50 T Homework Equations...
  47. J

    Show that the eigenvalues of the overlap matrix are positive

    Homework Statement The task is to show that the eigenvalues of overlap matrix \tilde S are positive. Homework Equations The overlap matrix is defined as (\tilde S)_{nm} = \langle \xi_n \vert \xi_m \rangle , with \xi_k being the base vectors of the wavefunction...
  48. C

    Angles from the positive x-axis

    Homework Statement In the problem sin-1 is 59.1. I have to give it from the positive x axis. Homework Equations The Attempt at a Solution Would it be 360-59.1? or 180-59.1? Thank you very much
  49. L

    Positive direction of the X axis?

    Homework Statement What are the x and y components of a vector a in the xy plane if its direction is 230° counterclockwise from the positive direction of the x-axis and its magnitude is 2 m? Homework Equations The Attempt at a Solution My main issue is I'm not sure where...
  50. H

    Positive Radius of Convergence

    Problem: Suppose that {a_{k}}^{\infty}_{k=0} is a bounded sequence of real numbers. Show that \suma_{k}x^{k} has a positive radius of convergence. Work: I have attempted to use the ratio test and failed. I am suspicious I can try the root test, but I am not sure how to work it...
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