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. P

    How Can We Prove That the Exponential Function is Always Positive?

    [SOLVED] Showing exp is positive... ... well not quite. This isn't actually homework, but here's what I'd like to prove: \forall n \in \mathbb{N} : \sum_{k=0}^{2n}\frac{x^k}{k!} \ge 0. I tried going about it through induction, but got into trouble quite early on: I couldn't prove that...
  2. E

    Smallest Number with 28 Positive Divisors

    Homework Statement Find the smallest number with 28 positive divisors. 28 = 14*2 or 7*4. So, it is either 2^13*3 or 2^6*3^3, right? Because 2^7 is manifestly larger than 3^2, it the latter, correct?Homework Equations The Attempt at a Solution
  3. K

    Positive definite real quadratic forms

    Q: Suppose q(X)=(X^T)AX where A is symmetric. Prove that if all eigenvalues of A are positive, then q is positive definite (i.e. q(X)>0 for all X not =0). Proof: Since A is symmetric, by principal axis theorem, there exists an orthogonal matrix P such that (P^T)AP=diag{c1,c2,...,cn} is...
  4. J

    Proving Limit Def. for Positive A & B: Help Needed!

    Homework Statement prove that if lim_{x\rightarrow c} f(x) = L, then there are positive numbers A and B such that if 0 < |x-c|< A, then |f(x)|< B 2. The attempt at a solution i know it's something to do with the limit definition, where for \epsilon > 0, there exists a \delta > 0 such...
  5. R

    Help Needed: Analyzing Limit as x Approaches Positive Infinity

    The problem is The limit as x approaches pos infinity ln(square root of x + 5) divided by ln(x) In the numerator only x is under the square root. I'm having trouble getting to this answer. If someone can take a look I would really appreciate it.
  6. F

    Write a Lisp program to calculate the sum of the first N positive integers

    Help! Please I am trying to write a Lisp program to calculate the sum of the first N positive integers where, for example, when N = 6 the sum of the first N = 21 Any Ideas?
  7. F

    Help - Lisp program to calculate the sum of first N positive integers

    Homework Statement Write a Lisp program to calculate the sum of the first N positive integers where, for example, when N = 6 the sum of the first N = 21. Homework Equations If you try this out in tlisp at http://www.ugcs.caltech.edu/~rona/tlisp/ please note that the syntax for N -...
  8. T

    Help Solve the Maths Challenge: Positive Integer with All Digits 1

    one of the "maths challenge" questions. one of the only ones i couldn't do :S I've tried for a good number of hours, but havnt found a way to do it. I feel any more time would just be brute forcing it which i wouldn't have time for in the exam anyways. hope you can help Homework Statement...
  9. T

    Is it possible to have a positive acceleration and slow down?

    (1) Is it possible to have a positive acceleration and slow down? (2) Is it possible to have a negative acceleration and speed up? I believe both answers are yes, but I need someone to clarify how. Please help. Thanks
  10. W

    How to prove that the positive irrationals are not denumerable?

    Since the positive reals aren't denumerable (or so do I read) and the positive rationals are, then that must mean the positive irrationals aren't. How do we go on about proving this?
  11. S

    Analysis - irrational number or positive integer

    Homework Statement Let n and k be positive integers. Show that k^{1/n} is either a positive integer or an irrational number. The Attempt at a Solution I set q = k^{1/n}. Then I set q = \frac{m}{p} . (Where m and p don't have common factors.) Then m^n = k * p^n . So then k is a factor...
  12. F

    Proving Constant Sequence of Positive Integers Starting with n

    Let n be a positive integer. Define a sequence by setting a_1 = n and, for each k > 1, letting a_k be the unique integer in the range [tex]0 \le a_k \le k-1[/itex] for which \displaystyle a_1 + a_2 + \cdots + a_k is divisible by k. For instance, when n = 9 the obtained sequence is \displaystyle...
  13. D

    Show that a definite integral is positive

    Show that \int_0^1 {x^n \sin \left( {\frac{{\pi x}}{2}} \right)} {\kern 1pt} dx > 0 for all {\rm{n}} \ge {\rm{0}} Basically, what i want to show is that over the interval (0,1), the integrand is above the x-axis, or positive. I will show that over the interval, both functions, x^n and...
  14. H

    Understanding Forces in Tug of War: Positive, Negative, Zero

    I solved the following question but I am doubtfull about my results In tug of war,the team that exerts a larger tangential force on the ground wins.Consider the period in which a team is dragging the opposite team by applying larger tangential force on the ground.List which of the following...
  15. M

    Negative or positive of a displacement and velocity

    I think when we talk about negative or positive of a displacement, we mean that the direction of this displacement which is either going downward or upward. But my question is how about when it says +/-velocity. Does it mean the direction or it means it speeds up or slows down? I think velocity...
  16. G

    What is the effect of a negative charge on the right hand rule?

    Yesterday I asked a question regarding the right hand rule and Lorentz law. I now understand how the right hand rule is applied but the examples I have looked at all involve a positive charge. My question is what effect does a negative charge have on the right hand rule? If for example a...
  17. rcgldr

    Why a negative times a negative is positive

    Since the other thread is closed, I thought I create one with a simple example of water in a tank that most people will understand. Imagine a tank designed to hold water with markers every inch from bottom to top. The marker halfway up the tank is chosen to be labeled zero. The next marker...
  18. S

    Why do 2 negatives make a positive?

    2x4 is the same as 4+4 right? they both equal 8 right? by what logic does -2 x -4 = 8. I know its a rule. but why?? shouldn't -4 + -4 = -8 or if it negates itself equal 0? :eek:
  19. Loren Booda

    Oo = -oo? positive infinity be equivalent to negative infinity?

    In what regard might positive infinity be equivalent to negative infinity?
  20. happyg1

    Negative vs Positive Determinants: What Does it Mean?

    Homework Statement I hope that I'm going to make sense here. I found the Jacobian of two functions by taking the partial of F1 w.r.t x, then y and same for F2. My professor did it by taking the partial of F1 w.r.t. y, then x, same for F2. So I have a 2x2 matrix. When i go to find the...
  21. edward

    Positive Proof Of Global Warming

    The latest photographic data.:smile: http://anthropology.net/files/warming.jpg
  22. V

    More Proofs: Prove that if n is an odd positive int., then n^2 = 1(mod 8)

    Homework Statement Prove that if n is an odd positive integer, then n^2\,\equiv\,1\,\left(mod\,8\right). Homework Equations Theorem: a\,\equiv\,b\left(mod\,m\right) if and only if a\,mod\,m\,=\,b\,mod\,m The Attempt at a Solution Using the theorem above: a\,=\,n^2 b\,=\,1,\,m\,=\,8...
  23. Andre

    The positive feedback factor of CO2

    In the other thread we / errm I discussed that theories cannot be proven but they can be falsified. Actually, without positive feedback, more CO2 is merely a mild friendly climate alleviator at the most So the issue here is the positive feedback factor of CO2 on the termination of ice...
  24. P

    Restoring force (negative or positive)

    Homework Statement First, I'll give a problem in context.. In anticipation of her first game, Alesia pulls back the handle of a pinball machine a distance of 5cm. The force constant of the spring in the handle is 200N/m. How much force must Alesia exert? Convert 5cm to 0.05m. F=kx...
  25. N

    Coulomb's Law (positive & negative charges)

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  26. M

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  27. murshid_islam

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  28. M

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  29. D

    The net force on a moving positive charge

    The net force on a moving positive charge... Homework Statement A magnetic field has a magnitude of 1.2 x10^-3 T, and an electric field has a magnitude of 5.4 x10^3 N/C. Both fields point in the same direction. A positive 1.8 µC charge moves at a speed of 2.9x10^6 m/s in a direction that is...
  30. E

    Positive Delta S: H2 + I2 --> 2HI, N2O4 from NO2

    Question: Which of the following would probably have a positive delta S value? He (g, 2atm) --> He (g, 10 atm) H2(g) + I2(s) --> 2HI (g) 2Ag(s) + Br2(l) --> 2AgBr(s) O2(g) --> O2(aq) 2NO2(g) --> N2O4(g) My answer: Well, I know that when a gas is pressurized, there are less states it...
  31. M

    Positive Quadrant Vector Space

    Homework Statement Show that the positive quadrant Q = ( (x,y) | x,y > 0 ) \in \mathbb{R}^2 is a vector space. Homework Equations Addition is redefined by (x_1,y_1) + (x_2,y_2) = (x_1 x_2, y_1 y_2) and scalar multiplication by c(x,y) = (x^c , y^c) The Attempt at a Solution There...
  32. S

    Negative and Positive Charges: A Deeper Look

    Can we, in principle, consider electrons as positive charges and protons as negative charges? How would our laws change if that was the case? Do you guys think that the convention of choosing electrons as negative charges and protons as positive changes was a mistake? Do we really need...
  33. K

    Positive integral implies bounded below?

    Homework Statement The integral of f on [a,b] exists and is positive. Prove there is a subinterval J of [a,b] and a constant c such that f(x) >= c > 0 for all x in J. Hint: Consider the lower integral of f on [a,b] Homework Equations The Attempt at a Solution I don't see how...
  34. S

    Force, Electric Field, and Positive Particle

    Homework Statement A long line carrying a uniform linear charge density 50.0 microcoulombs/m runs parallel to and 10.0 cm from the surface of a large, flat plastic sheet that has a uniform surface charge density of -100 microcoulombs/m^2 on one side. Find the location of all points...
  35. J

    Adding trig functions for positive output

    Hello All, Here's a strange question for you. Is there any possible way to add two or three sine wave functions together so that the resulting wave never goes below the positive Y axis of the graph? These functions can be whatever frequency or phase necessary, just no vertical offset. I am...
  36. E

    Operational Amplifier with positive feedback problems

    Homework Statement I have some problems determining the tension output value for this circuit and this confusion comes from the presence of positive feedback and an alternate current.Since I'm used to negative feedback circuits and direct current it confuses me a bit,so any help is deeply...
  37. E

    How does positive feedback works in opamp circuits?

    I was wondering,how does positive feedback works in opamp circuits?Like is there any formula for calculating positive feedback?I know that with negative feedback we have Vp=Vn but I don't know how it works with positive feedback!Thanks for the reply!
  38. A

    Need to prove that the following integral is positive

    I need help proving that the following (double) integral is positive: int(limits from -infinity to +infinity) f(b) int(limits from b to +infinity) [e^{-(x-mean)/(2 *variance)}]/sq root(2 *pi *variance) dx db thanks
  39. D

    How to prove trace(A.A*) is positive

    Hello I'd like to know how to prove that the trace of A.A* is positive. I don't really know how to handle the imaginary part of it. If A has any complex number in it, is it possible to get traces like 10-2i? If yes, do I consider it as a positive number or negative?:zzz: Thanks in advance
  40. A

    Reference angles always positive?

    Simple question. Are reference angles always positive??
  41. K

    Work Done on a Bucket in a Well

    "A rope exerts a force on a bucket as the bucket is raised up a well." Is the work done on the bucket positive or negative? Now, I know that the is a tension force in the rope that must overcome weight to accelerate the object up the well. Also, work is positive if the force exerted is in the...
  42. J

    Does Convergence Rate Affect Series Behavior?

    Let (infinity)(sigma)(n=1) = An be a series with positive terms such that lim(n -> infinity) = (An+1)/(An) = L < 1 a) Let L < r < 1. Show that there is an N > 0 such that for all n > N, we have (An+1)/(An) < r b) Show that Ak+N < or = ANr^k for k = 1, 2... c) Show that lim (k ->...
  43. N

    Gravitational energy : positive or negative ?

    I know that gravitational energy is a delicate topic in GR. It is true that the localisation of gravitational energy is not possible in GR but it should at least be possible to determine correctly the sign of the gravitational energy. I found the following article in arxiv.org, nl...
  44. V

    Explaining the Nucleus: Positive Charges & Observations

    Can you tell me the answer to this question? Why would the scientific community resist the concept of a nucleus full of positive charges and what observations helped them explain this design. Thanks, v
  45. I

    Finding the Positive Number A in a Parabola Problem

    alright so here is the problem. The parabola y=x**2+3 has two tangents which pass through the point (0,–2). One is tangent to the to the parabola at (A,A2+3) and the other at (–A,A2+3). Find (the positive number) A. i've attempted this problem several times but haven't been able to find the...
  46. R

    Proving Convergence of a Series with Positive Terms

    hi, I found this problem in Rudin, and I just can't figure it out. It goes like this: Prove that the convergence of \sum a_n a_n \geq 0 implies the convergence of \sum \frac{\sqrt{a_n}}{n} I tried the comparison test, but that doesn't help because I don't know what the limit \lim_{n...
  47. M

    Proving P(n) for Every Positive Even Integer

    Hello everyone. I'm trying to set this problem up to prove by induction but having some issues. Suppose that for some Predicate P(k), you first prove that P(1) is true, and then you do the following. You prove that, for every positive even integer k, if P(i) is true for all odd integers i...
  48. C

    What is the cars acceleration, assuming forward is positive?

    today is my first day here so if i violate any rule that apply in this forum please forgive me.. the question is Dr. Silverstein is driving a 1.95 * 10^3 kg car at 55.0Km/hr. He slams on the brakes and comes to rest in a distance of 17.0 m Assume that Dr. Silverstein has a mass of 75.0 kg...
  49. T

    Solving for Equality with Positive a and b

    hello everyone, I have a problem, if anyone can get me started. Thanks I have to show this equality knowing that a and b are positive and they do not euqal 0: (a^{2}+a^{\frac{4}{3}}b^{\frac{2}{3}})^{\frac{1}{2}} + (b^{2}+a^{\frac{2}{3}}b^{\frac{4}{3}})^{\frac{1}{2}}...
  50. S

    MATLAB Eigenvalues of Positive Definite matrices - &MATLAB

    I'm trying to create an algorithm in MATLAB, but I have a problem. According to theory, if G is a positive definite matrix, then it's eigenvalues are positive real numbers. I'm using function EIG() to calculate the eigenvalues and eigenvectors of matrices, but I almost always take and negative...
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