Variables Definition and 1000 Threads

In mathematics, and in other disciplines involving formal languages, including mathematical logic and computer science, a free variable is a notation (symbol) that specifies places in an expression where substitution may take place and is not a parameter of this or any container expression. Some older books use the terms real variable and apparent variable for free variable and bound variable, respectively. The idea is related to a placeholder (a symbol that will later be replaced by some value), or a wildcard character that stands for an unspecified symbol.
In computer programming, the term free variable refers to variables used in a function that are neither local variables nor parameters of that function. The term non-local variable is often a synonym in this context.
A bound variable is a variable that was previously free, but has been bound to a specific value or set of values called domain of discourse or universe. For example, the variable x becomes a bound variable when we write:

For all x, (x + 1)2 = x2 + 2x + 1.
or

There exists x such that x2 = 2.
In either of these propositions, it does not matter logically whether x or some other letter is used. However, it could be confusing to use the same letter again elsewhere in some compound proposition. That is, free variables become bound, and then in a sense retire from being available as stand-in values for other values in the creation of formulae.
The term "dummy variable" is also sometimes used for a bound variable (more often in general mathematics than in computer science), but that use can create an ambiguity with the definition of dummy variables in regression analysis.

View More On Wikipedia.org
Recent contents Top users
  1. C

    Classical mechanics, Hamiltonian formalism, change of variables

    Homework Statement This problem has to do with a canonical transformation and Hamiltonian formalism. Below is my attempt at solving it, but I am not too sure about it. Please help! Let \theta be some parameter. And X_1=x_1\cos \theta-y_2\sin\theta\\ Y_1=y_1\cos \theta+x_2\sin\theta\\...
  2. R

    MHB Heat and Temperature Equations-Separation of variables

    I really don't how to start this question. Please help me.
  3. U

    Finding the Variables for f(x,y)=e^{xy}

    Homework Statement Let f(x,y)=e^{xy} Variables u and v are defined by u=x^{3}-y^{3} , v=x^{2}+xy Find the values of \deltaf/\deltau and \deltaf/\deltav at the point where x=-1 and y=2 Homework Equations N/A The Attempt at a Solution At first I thought that I'd have to write...
  4. H

    Singularities of two variables rational functions

    Homework Statement Let p(x,y) be a positive polynomial of degree n ,p(x,y)=0 only at the origin.Is it possible that the quotient p(x,y)/[absolute value(x)+absval(y)]^n will have a positive lower bound in the punctured rectangle [-1,1]x[-1,1]-{(0,0)}? Homework Equations The Attempt at a...
  5. M

    MHB Discrete or Continuous: 4 Random Variables

    Classify the following as discrete or continuous random variables. (A) The number of people in India (B) The time it takes to overhaul an engine (C) The blood pressures of patients admitted to a hospital in one day (D) The length of a centipede
  6. C

    (easy) Finding variables with mirror equation

    This isn't exactly a homework problem, per se, but this was a district assessment I already took today. I was confident that I would get a good grade, but it turns out I got a measly 65%. I don't remember the exact wording, but I do remember the general idea of it.Homework Statement There are...
  7. H

    Is There a Positive Constant for a Polynomial Inequality with Two Variables?

    Hi Let p(x,y)≥0 be a polynomial of degree n such that p(x,y)=0 only for x=y=0.Does there exist a positive constant C such that the inequality p(x,y)≥C (IxI+IyI)^n (strong inequality!) holds for all -1≤x,y≤1? The simbol I I stands for absolute value.
  8. P

    Determinant of a general matrix with variables.

    Hi, Homework Statement I was asked to find the determinant of the following two matrices (please see attachment). Homework Equations The Attempt at a Solution I know that the determinant of the matrix on the left is [(-1)^(n-1)]*(n-1), but I have no idea how to formally derive...
  9. P

    Algebra- find solution using two variables

    Homework Statement A chemist ran out of a 72 ml solution of 12% alcohol. All that is left in the lab is 8% alcohol and 20% alcohol. How many ml of 8% and 20% would be needed to make a 72 ml solution of 12%? Homework Equations The Attempt at a Solution 8x + 20y = 12
  10. P

    Order of variables in a Jacobian?

    Hi, Homework Statement I was hoping someone could please explain the order of variables in a Jacobian. I mean, once the dependent and independent variables have been identified, how should the Jacobian be formulated. For instance, supposing I have two implicit functions F(x,y,u,v) and...
  11. G

    Epsilon/Delta Proof With 2 Variables

    Homework Statement Prove: f(x,y) = \frac{x(x^{2}-y^{2}}{(x^{2}+y^{2}} if (x,y) \neq (0,0) 0 if (x,y) = (0,0) is continuous at the origin Homework Equations \forall \epsilon > 0 \exists \delta > 0 s.t. if |(x,y)| < \delta then |f(x,y)| < \epsilon (Since we are proving...
  12. O

    What are the correct labels for the variables in the bar chart?

    I need to drag and drop all the labels into the relevant boxes by the bar chart. Three spaces will be left empty because there is anything to describe them. (See the attachment) I was thinking: title empty empty smalles difference between ... empty independent variable dependent variable...
  13. R

    Adding variables with same exponents

    Homework Statement solve. .2y^3 + .6y^3 - .5y^3 I believe the answer to be .3y^3 Homework Equations The Attempt at a Solution i got the answer to be .8y^3 - .5y^3 = .3y^3 I think this is correct, I'm not sure, please let me know if I finished this correctly.
  14. J

    Stats: Covariace of 2 Random Variables

    Homework Statement Let X ~ Exponential(3) and Y ~ Poisson(5). Assume X and Y are independent. Let Z = X + Y. Compute the Cov(X,Z).Homework Equations I know Cov(X, Z) = E(XZ) - E(X)E(Z). But how do I compute E(XZ) and E(Z) ?? Since for E(XZ), I would need the pdf/pmf (Exp is abs cts, while...
  15. M

    Calculating Density Function of Joint Independent Exponential Random Variables

    X and Y are independent, exponentially distributed random variables - with possibly different parameters Determine the density func. of Z = X / Y How to attack ?
  16. J

    Solving for time with these variables

    Ok, I think I'm missing some math knowledge and is to why I can't solve this.. or maybe I'm just burnt out for the day.. However here is the situation: Mass = 0.06kg Impact Velocity = 7.34m/s Final Velocity = 0m/s Displacement from impact velocity and final = 0.099m Acceleration = 9.8...
  17. Y

    Sum of N geometric variables with changing probability

    Homework Statement Ʃ(A-i)/(N+1-i) sum of i=1 to N Homework Equations How do I solve this series for all 0<N<A cases. This series is the sum of N geometric variables of changing probability. I'd appreciate any help
  18. M

    Solving a PDE by Separation of Variables - Troubling Condition

    Homework Statement Hopefully no one will mind me posting this as an image. But here it is in tex: Using separation of variables, find the function u(x,t), defined for 0\leq x\leq 4\pi and t\geq 0, which satisfies the following conditions: \frac{\partial^2 u}{\partial...
  19. J

    Solving by substitution for multiple variables

    Homework Statement I have four equations and have four variables. I need to solve for each of the variables. I am having difficulty figuring out how to do this. My equations are here. http://imgur.com/EOA8I Homework Equations \frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1 The Attempt...
  20. Mandelbroth

    Regarding continuous stochastic variables and probability

    One of my math teachers discussed stochastic ("random") variables today. In an example, he discussed the probability of picking a random number n, such that n\inℝ, in the interval [0,10]. He proceeded to say that the probability of picking the integer 4 (n = 4) is 0, supporting his claim with...
  21. S

    Solve for trig equation with 2 variables

    Homework Statement Homework Equations The Attempt at a Solution I can solve the first part of the question. -2 ≤ k ≤ 2 because -1 ≤ sin(x) ≤ 1. How do I solve the second part of the question? Thanks.
  22. J

    How to solve for four variables when two have first and second degrees

    Homework Statement does anyone know how to solve this equation for just x? x + x^2 = a^2*b^2 - 2.01j - j^2 - 15.132 it's possible right? because I'm trying to solve for four variables using four equations but two of my variables will have a first plus a second degree The...
  23. J

    PDE Separation of Variables with Nonzero Boundary Conditions

    Homework Statement Solve the diffusion equation: u_{xx}-\alpha^2 u_{t}=0 With the boundary and initial conditions: u(0,t)=u_{0} u(L,t)=u_{L} u(x,0=\phi(x) The Attempt at a Solution I want to solve using separation of variables... I start by assuming a solution of the form...
  24. H

    Identifying Independent and Dependent Variables

    Hi, I am trying to identify the independent and dependent variables in the following experiment: Two groups of patients (Epileptic and Normal) are exposed to varying wavelengths of light and their neural response is quantified and recorded. I am using...
  25. E

    Partial Derivative Product with variables as functions

    Homework Statement I'm trying to understand how a certain substitution can be made with regards to taking the partial derivative of a function product when the variable I am differentiating by is a function itself.Homework Equations (∂/∂p) (v(p)p(x,t)) = v(p) + (∂v/∂p)pThe Attempt at a...
  26. K

    Calculating Conditional Expectation of X,Y,Z: Triangle Inequality

    1. Let T = (X,Y,Z) be a Gaussian for which X,Y,Z for which X, Y, Z are standard normals, such that E[XY] = E[YZ] = E[XZ] = 1/2. A) Calculate the characteristics function Φ_T(u,v,w) of T. B) Calculate the density of T. 2. Let X and Y be N(0,1) (standard normals), not necessarily...
  27. fluidistic

    Circular membrane, PDE, separation of variables, coefficients.

    Homework Statement I must find the oscillations of a circular membrane (drum-like). 1)With the boundary condition that the membrane is fixed at r=a. 2)That the membrane is free. Homework Equations The wave equation \frac{\partial ^2 u }{\partial t^2 } - c^2 \triangle u =0...
  28. D

    MHB Solving Real Number Variables & Parabola Equations

    This question was asked in my exam and I could not answer it. I would like to know how it can be solved. If $l$ and $m$ are variable real numbers such that $5l^2+6m^2-4lm+3l=0$, then a variable line $lx+my=1$ always touches a fixed parabola, whose axis is parallel to the x-axis. (a) Find the...
  29. D

    I'm not sure what you mean by roots in the exponent of u. Can you clarify?

    Examine for which u \in \mathbb R the series \sum\limits_{n=1}^\infty \frac {(1+(-1)^n)^n}{n^2} |u|^{\sqrt{n}(\sqrt{n+1})} converges. What I found out so far: (1+(-1)^n) alternates between [0;2], that means that the whole series becomes zero for the even n. The interesting part are the odd n...
  30. M

    Mathematica Mathematica plotting with a slightly complicated relationship between variables

    Hi, So here's my latest problem as I get to grips with Mathematica. I will give a simpler version of the one I am actually doing. I started with a closed set of differential equations. Consider the following equations a'(t)=P*b(t) b'(t)=P^{2}*a(t) with known initial conditions and P is a...
  31. H

    Qq- ->qq- differential cross section and mandelstam variables

    qq- --->qq- differential cross section and mandelstam variables Homework Statement for the problem statement please look the attachement Homework Equations The problem is asking to express the mandelstam variables in temrs of the scattering angle θ.I would like to ask the quastion...
  32. P

    How to solve general forces equations as variables?

    Okay, so we were doing forces, and my teacher had this question: In an atwood machine, a massless, non stretching string passes over a frictionless peg, one end of the rope is connected to object m1, and the other end to object m2 (heavier). When the system is released from rest, m2 goes...
  33. A

    Discrete Bivariate Random Variables

    Here is the question: Consider the experiment of rolling two tetrahedra that are unfair in the sense that each has the following probabilities for each of the four faces: P{1 dot}=1/10 P{2 dots}=2/10 P{3 dots}=3/10 P{4 dots}=4/10 Let X be the total of the outcomes in the two...
  34. D

    Force Equations: All Variables Given in Pictorial Form

    Homework Statement All variables are given in the pictures. Homework Equations Nothing more than simple force equations. The Attempt at a Solution I attempted it on my own, but I don't know if the answers are right.
  35. M

    Mathematica Defining 2x2 Matrices with Variables for Solving DEs

    Hi, I have a bunch of closed differential equations that I want to solve. The variables of the DEs are 2x2 matrices. So, I want to enter some 2x2 matrices of variables and then use NDSolve to get the solution. How should I define a 2x2 matrix with four variables inside it? I tried...
  36. D

    Everyday analogy why hidden variables can’t explain entanglement

    Everyday analogy why hidden variables can’t explain entanglement I tried to come up with an everyday “obvious” analogy that explains why a hidden variable theory cannot explain quantum entanglement. Here’s the story: There are two guests and one moderator on a stage. The moderator...
  37. 6

    Laplace Equation Solved by Method of Separation of Variables

    Homework Statement Homework Equations Assume the solution has a form of: The Attempt at a Solution It looks like a sine Fourier series except for the 2c5 term outside of the series, so I'm not sure how to go about solving for the coefficients c5 and c10. Any idea?
  38. W

    How to calculate inverse cosine of two variables

    Hi, all I am looking into inverse cosine operations. I have a question like follows: Let x and y be two variables of degrees, how to separate equation arccos(x+y) into an equation that contains x and y separately? Such as arccos(x+y) = f1(...x) + f2(...y)? Thank you very much for your...
  39. chisigma

    MHB An interesting two variables function....

    An interesting question has been posted in... Infinite Series Conditional Converging ... about the following two variables function... $\displaystyle \sigma(x,y)= \sum_{k=1}^{\infty} \frac{1}{(k+x)\ (k+y)}$ (1) ... and in particular it has been requested if the domain of $\sigma(*,*)$ must...
  40. T

    Probability question ,Random variables and probability distribution

    I'm completely lost on this probability problem, Homework Statement A Box contains 5 indiscernible CDs.It is known that among them 2 are for children .So in order to find the first children's CD ,they are tested one after the other (successively ),Denote by X the random variable which...
  41. E

    How Do You Derive u=p/ρ₀c₀ and ρ=p/c₀² from 1D Wave Equations?

    Given The 1D wave equations p_{x}'' - (1/c_{0}^2)p_{t}'' = 0 u_{x}'' - (1/c_{0}^2)u_{t}'' = 0 ρ_{x}'' - (1/c_{0}^2)ρ_{t}'' = 0 and linearised continuity and momentum equations ρ_{t}' = -ρ_{0}u_{x}', ρ_{0}u_{t}'=-p_{x} how may one derive the following two equations? u=p/ρ_{0}c_{0}...
  42. P

    Dynamic Programming with 2 state variables

    Homework Statement Derive the Euler Equation of the dynamic programming problem: \[max_{\{ z_t \}^\infty_{t=0}} \sum_{t=0}^{\infty} \delta^t f(x_t, y_t, z_t) \] subject to: x_{t+1} = g_1(x_t, y_t, z_t), \ y_{t+1} = g_2(x_t, y_t, z_t), \ x_0 = x^0, y_0 = y^0 and where \delta <1...
  43. A

    Limit in two variables polar vs cartisiean differ in result

    Hello I have the limit lim (x^9 * y) / (x^6 + y^2)^2 (x,y)---> (0,0) when I use polar the final result is limit = lim (r^6 cos^9 (theta) sin (theta) ) / (r^4 cos^6 (theta) + sin^2 (theta)) r--->0 and substituting r = 0 , it will give zero * I tried it on wolfram...
  44. M

    Maxima and minima of functions of two variables

    Homework Statement Locate all relative maxima, relative minima ,and saddle points if any. f(x,y)=ysinx fx(x,y)=ycosx fy(x,y)=sinx ycosx=0 sinx=0 y=0 x=0,∏,2∏... up until infinity Critical points at (0,0),(∏,0),(2∏,0)... fxx(x,y)=-ysinx...
  45. C

    Characteristic function of Sum of Random Variables

    Homework Statement Let X,W,Y be iid with a common geometric density f_x(x)= p(1-p)^x for x nonnegative integer and p is in the interval (0,1) What is the characteristic function of A= X-2W+3Y ? Determine the family of the conditional distribution of X given X+W? Homework Equations...
  46. N

    Integration of random variables

    Homework Statement f(x,y)= (4/5)(x+3y)exp(-x-2y) for x,y, >0 Find E[Y|X] Homework Equations E[Y|X] =integral y *f_xy (x,y)/ f_x (x) dy The Attempt at a Solution f_x (x) = integral [o,∞] [4/5](x+3y)exp(-x-2y) dx = (2x+3)/(5exp(x)) When taking the integral of y[(4/5)(x+3y)exp(-x-2y)] /...
  47. S

    Sum of binomial random variables

    Homework Statement let y_1 and y_2 be iid bin(5,1/4) random variables let v=y_1+2*y_2 and u = 3*y_1 -2y_2 find f_uv (u,v) and the cov(u,v) Homework Equations f_y (y) = (5 choose y) (1/4)^y (3/4)^5-x for x=0,1,2,3,4,5 covariance=E(uv)-E(u)E(v) The Attempt at a Solution...
  48. C

    Convex Function on Many variables on an interval

    Homework Statement Show that f(x) = x1x2 is a convex function on [a,ma]T where a \geq 0 and m \geq 1. Homework Equations By definition f is convex iff \forall x,y\in \Re \quad \wedge \quad \forall \lambda :\quad 0\le \lambda \le 1\quad \Rightarrow \quad f\left( \lambda x+(1-\lambda...
  49. B

    Continuous and discrete variables with a copula?

    Hi, I have 3 correlated variables that I wish to model with a copula function. 2 of the variables are continuous and 1 is discrete. My question is, generally speaking can you model continuous and discrete variables within the same copula? Yes/No? Thanks
  50. H

    Some thoughts on the hidden variables interpertation

    Hi, another thread talking sbout QM interpertations sparked my interest on the subject. Now let's assume that we have electrons in a box, it could be anywhere inside. And let us assume that the electrons do indeed have unique positions instead, that each electron has a set of three continuos...
Back
Top