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. R

    Eigenvalues of positive definite (p.d) matrix

    If C = A +B where A,B are both p.d, than C is p.d and its eigenvalues are positive. Waht can you say about the relationship between the eigenvalues of C, and A,B ? Thanks.
  2. M

    If a,m and n are positive integers with m<n

    well this is the question... if a,m and n are positive integers with m<n, then (a^(2^m)+1) is a divisor of (a^(2^n)-1)... I started using induction and it works for the first step... but for the second one i do not know if i can make induction on m... any hint would help.. thanks :)
  3. S

    Why does imidazolium ring contain a positive charge?

    Just interested how this positive charge occurs. Thank you :smile:
  4. T

    Right Hand Rule - Positive or Negative Action

    Homework Statement http://img41.imageshack.us/i/photolu.jpg/ Homework Equations Right Hand Rule The Attempt at a Solution I have to find the moments at B. I know I have to use the right hand rule to figure out which force has a positive and which force has a negative action...
  5. D

    Cycle Length of the Positive Powers of Two Mod Powers of Ten

    The positive powers of 2 mod 5^m cycle with period 4*5^(m-1), which you can prove by showing that 2 is a primitive root mod powers of 5. I want to prove that the positive powers of two, mod 10^m, also cycle with this same period. How do I go from this powers of 5 result to powers of 10...
  6. M

    Hermitian positive definite matrix

    Let P and Q be Hermitian positive definite matrices. We prove that x*Px < or eq. x*Qx, for all x in C^n (C : complex numbers) if and only if x*Q^-1 x < or eq. x*P^-1 x for all x in C^n. I guess I should use the definition of a hermitian positive definite matrix being x*Px > 0 , for all x in...
  7. Q

    Is energy always positive and dependent on observer's frame of reference?

    I was under the impression that energy had to be positive. Yet it seems we are still forced to use negative energies since we set the potential to be 0 at an infinite distance away. And the only reason we don't set the potential energy to zero at the origin of the source is because there is a...
  8. N

    Is there a way of proving that all positive numbers have a real square root?

    Homework Statement My prof showed us the proof that sqrt2 is not a rational number. She said, however, that we haven't proved that it is irrational, because we haven't proved that sqrt2 exists. How would we go about proving this? Homework Equations N/A The Attempt at a Solution...
  9. H

    Understanding the Nature of Electric Charges: A Cat and Rubber Boots Experiment

    A cat rubs against a pair of rubber boots. What charge is found on both? Explain. Is all rubber non conductive or would I say the cat has a negative charge and the boots a positive charge? Thank you.
  10. S

    Where n is an odd positive integer

    I'm studying for a test. In doing one of the old tests and it had a question that I couldn't do. Let T: Rn \rightarrow Rn be an operator on Rn, where n is an odd positive integer. How do I prove T has at least one eigenvector in Rn
  11. L

    Positive or negative velocity and acceleration

    Homework Statement A motion detector is placed on the top of a ramp sloping down. A cart is placed at the other end of the ramp (bottom of the ramp). The cart is pushed up the ramp towards the motion detector (top of ramp), and stopped at it's highest point. Homework Equations 1. Is the object...
  12. E

    In free-fall acceleration, how do I figure when g is positive or negative?

    In free-fall acceleration, how do I figure when "g" is positive or negative? Homework Statement My textbook is confusing me a bit. In general, when would "g" be positive and when would be negative? I thought it was when the particle was falling downward, it was positive and when it's going...
  13. R

    Electric flux (positive, negative, or zero?)

    Homework Statement Imagine a positive point charge on the left side of the picture and an area defined by a loop on the right. I was asked to draw and label the area vector and sketch the electric field lines due to the point charge, which I did. The next questions asks: Is the electric...
  14. K

    Negative time and positive time

    how do i find at what negative time and positive time does the particle pass throught the origin?
  15. N

    Converging Series and Derivative Analysis for Positive Terms

    sum(1/(n(n^2-1)^(1/2)),n=2,infinity) first derivative <0 for x>=2 I(1/(x(x^2-1)^(1/2)),x,2,infinity) x=secT, dx=secTtanT I(secTtanT/(secTtanT),T) ?
  16. E

    Another positive operator proof

    Homework Statement Suppose that T is a positive operator on V. Prove that T is invertible if and only if <Tv,v > is >0 for every v ∈ V \ {0}. Homework Equations The Attempt at a Solution If T is invertible, then TT-1=I.Now let v=v1+...+vn and let Tv=a1v1+...+anvn. Now <Tv...
  17. E

    Positive integer proof

    positive operator proof Homework Statement Prove that if T ∈ L(V) is positive, then so is Tk for every positive integer k. Homework Equations The Attempt at a Solution Let v=b1v1+...+bnvn. Now since T is positive, T has a positive square root. T=S^2. <S^2v, v>=<S^2v1...
  18. daniel_i_l

    Positive reinforcement gives me the creeps

    When a child does something favourable in the eyes of his parents, even something insignificant, and gets heaped with praise it gives me the creeps. I know that it's a useful educational tool but when every small action is rewarded it seems sort of like brainwashing. The kid is doing things to...
  19. E

    Prove Positive Operators Sum is Positive on V

    Homework Statement Prove that the sum of any two positive operators on V is positive.Homework Equations The Attempt at a Solution This problem seems pretty simple. But I could be wrong. Should I name two positive operators T and X such that T=SS* and X=AA*? I have a bad history of seeing a...
  20. D

    Converging Uncountable Sum of Positive Reals

    Does there exist a converging uncountable sum of strictly positive reals?
  21. M

    Let X be a positive variable with E(X) =5 and E(X)^2 =31.25

    Please find an upper bound for P(X>=10) using Markov's and Chebyshev's Please state which is which. I'm not very good at stats and this is a homework problem :P Thanks!
  22. A

    Sum of the fourth powers of the first n positive integers

    Homework Statement Find a formula fo the sum of the fourth powers of the first n positive integers n ∑ i^4 (i=1) Justify your work using mathematical induction Homework Equations so i know the formula for the sum of the cubes of the first n positive integers k=n+1 ∑...
  23. N

    Another necessary condition for Positive Semidefiniteness?

    Hi everyone in this sub forum, I'm wondering if the following 'rule' (theorem?) is correct: For a hermitian Positive Semidefinite (PSD) matrix A=(a_{ij}), \max_{i,j\le n} |a_{ij}|=\max_{i\le n}a_{ii}. The reason for this intuition (It may be a well known result, I'm very sorry in this...
  24. S

    Electromagnetic version of the positive energy theorem?

    Hello, I've been quite avidly reading about one of the spectacular recent joint achievements of physics and pure math. The positive energy theorem [1,2,3] concerns the large-distance asymptotic behaviour of the gravitational field due to a localised distribution of mass-energy. I think I...
  25. N

    How to show that expectation value is always positive?

    Homework Statement In quantum mechanics, how to show that the expectation value is always positive? Homework Equations The Attempt at a Solution
  26. T

    Calc Angle b/w Radius Vector Point & +x Axis: What Does That Mean?

    Calc. Angle between radius vector point and positive x axis? What does that mean? Homework Statement The cartesian coordinates of a point in the xy plane are x = −8.96 m, y = −1.75 m. Calculate the angle  between the radius- vector of the point and the positive x axis (measured...
  27. maverick280857

    Exploring the Meaning of Positive and Negative Energy in the Klein Gordon Field

    Hi everyone The Hamiltonian of the Klein Gordon field can be written as H = \frac{1}{2}\int d^{3}E_p \left[a^{\dagger}(p)a(p) + a(p)a^{\dagger}(p)\right] and we have [H,a(p')] = -E_{p'}a(p') [H,a(p')] = +E_{p'}a^{\dagger}(p') The book I'm reading states that What does this mean? Thanks.
  28. Bob_for_short

    Positive charge atomic form-factor

    IT IS A POLL! I would like to learn if you've ever heard of the positive charge atomic form-factor before my asking this question. The positive charge atomic form-factor fnn'(q) stands at the nucleus charge Z and describes the positive charge cloud in atoms for elastic scattering at large...
  29. S

    Proving -x = x with Positive Even Integer n in R

    Homework Statement Let R be a ring and suppose there exists a positive even integer n such that x^n = x for every x in R. Show that -x = x for every x in R. Homework Equations The Attempt at a Solution I solved the case where n = 2. Let x be in R. (x+x)^2= x+x = 2x...
  30. N

    Condition for a matrix to be Positive semi-definite

    Hi everyone, I know that for a matrix to be Positive semi-definite (A>=0) (PSD), the elements on the principle diagonal (upper left corner to right bottom corner) must be non-negative (i.e., d_ii>=0). But I wonder if there exists any condition to be satisfied by the elements on the secondary...
  31. F

    Why the at term on the exponential turned positive

    Firstly, I don't get why the at term on the exponential turned positive (red arrow).. can someone explain that please? And how do I start on this? How do I split it up such that I can do it for t>0 and t=<0? Do I just integrate e^2t between -inf and 0 and integrate e^-t...
  32. M

    One point compactification of the positive integers

    How do we show the one point compactification of the positive integers is homeomorphic to the set K={0} U {1/n : n is a positive integer}? Say Y is the one point compactification of the positive integers. I know Y must contain Z+ and Y\Z+ is a single point. Also Y is a compact Hausdorff...
  33. D

    How does one integrate for positive beta and real b ?

    How does one integrate \int_0^\infty e^{-\beta x^2}\cos{(bx)} dx for positive beta and real b ? I was thinking maybe differentiation under the integral sign would do the trick, but I can't get anywhere.
  34. B

    Electricity: Positive to Negative or Negative to Positive?

    Lets say you have a battery and connect wires to each of the terminals. Now you bring both of the wires together to create a spark. Is the spark jumping from positive to negative (current) or from negative to positive (electron flow). Thanks!
  35. L

    Work done by spring forces - positive or negative

    work done by spring forces -- positive or negative I have gotten the sign wrong on every single spring force-related problem. I'm pretty sure I'm working out the problems correctly, but the answer turns out to be negative when I have it positive, or positive when I have it negative. Of...
  36. F

    Combinatroics 4-permuations of positive integers

    Homework Statement How many 4-permutations of the positive integers not exceeding 100 contain three consecutive integers k, k+1, k+2, in the correct order: a) where these consecutive integers can perhaps be separated by other integers in the permutation? b) where they are in...
  37. K

    Seven digit base eight positive integer puzzle

    N is a seven digit base-8 positive integer having the form ABCDEFG that uses each of the nonzero base-8 digits 1 to 7 exactly once, and satisfies these conditions: (i) ABCDEFG is divisible by 7. (ii) ABCDEF is divisible by 6. (iii) ABCDE divisible by 5. (iv) ABCD is divisible by 4. (v)...
  38. B

    Why is the Square Root of a Real Number Positive?

    Hi, Apologies for the trivialness of the question, but I'm not so great at this. I was wondering why the square root of a real number is positive. Why is sqrt(9) = 3, and not -3 as well, since (-3)² would give 9. Is it just a condition you set, that the function values must be positive? At...
  39. E

    Finding the positive x-value on a hyperbola

    Homework Statement The curve y^2-3xy+2x^2=4 is a hyperbola with axes rotated from the standard position. Use Newton's Method to find the positive x-value to four decimal places for the point on the hyperbola where y=1. Homework Equations Newton's Method The Attempt at a Solution...
  40. K

    Best way to easily make positive ions?

    How do you make positive ions? I found a kit device that is made of a bunch of capacitors and diodes that's supposed to make negative ions (it says to reverse the diodes to make positive ions) how does this work? Wikipedia and HowStuffWorks weren't much help. Wikipedia explained what diodes...
  41. T

    Inner Prod Space, Positive Definite Proof

    Homework Statement Let H be an inner product space. Let T:H->H be a linear, self adjoint, positive definite operator. Fix h in H and let g = T(h) / square root (1 + (T(h),h)). for h in H Show that the operator S:H->H defined by S(v) = T(v) - (v,g)g for v in H is positive definite...
  42. S

    For All Positive Numbers: Is y the Solution?

    Homework Statement There exists y > 0 such that [y^{2} = x if and only if x > 0]. This means that "there is some positive number whose square equals all positive numbers." - St. John College, Oxford The Attempt at a Solution I am not sure about this statement "- - some positive number whose...
  43. I

    Inequality involving positive definite operator

    1. Given that |\langle f|g\rangle|^2 \leqslant \langle f|f\rangle\langle g|g\rangle prove that |\langle f|H|g\rangle|^2 \leqslant \langle f|H|f\rangle \langle g|H|g\rangle where H is a Hermitian and positive definite operator. [b]3. I tried to identify H|g\rangle as a state and put...
  44. A

    Real Symmetric Positive Definite Matrices

    Homework Statement Let A be a real symmetric positive definite matrix. Show that |aij|<(aii+ajj)/2 for i not equal to j. Homework Equations The Attempt at a Solution I really don't even know where to start with this. I think that aii and ajj must both be > 0 since they are on the...
  45. C

    Calculating Current given the number of electrons and positive ions

    Homework Statement In a fluorescent tube of diameter 3 cm, 10 *1018 electrons and 2.5 * 1018 positive ions (with a charge of +e) flow through a cross-sectional area each second. What is the current in the tube? Homework Equations Current is I = (delta Q)/(deta T) The Attempt at...
  46. P

    Is the positive terminal of a battery positively charged?

    Does the positive electrode of a Daniel cell (the Copper electrode) actually have a net positive charge when the electrodes are not connected by a conducting material such as a wire? If not, does it have a net charge at all and how does this charge compare to the negative terminal? Finally...
  47. O

    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...
  48. 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...
  49. 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...
  50. 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...
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