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.

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  1. A

    Isolate for Angle With Variables

    Homework Statement Isolate for the angle. Do not sub in numbers, isolate the angle, θ . Use of trig identities required. Homework Equations m_{2}g=m_{1}gsinθ-μm_{1}gcosθ We are given the trigonometric identities: The Attempt at a Solution I have attempted everything from squaring both...
  2. J

    Difficulty with summation of non-central chi-squared random variables

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  3. Y

    Bivariate Transformation of Random Variables

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  4. R

    Probability that sum of two random variables is greater than 1

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  5. K

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  6. D

    MHB Change of variables heat equation

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  7. P

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  8. P

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  9. S

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  10. C

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  11. skate_nerd

    MHB Non-continuous integrals and discrete variables

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  12. F

    MHB Separation of variables, can't get y out of exponent

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  13. F

    MHB Separation of variables, constant in front of term

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  14. M

    Sum of independent Random Variables

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  15. E

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  16. N

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  17. N

    MHB Mgf of continuous random variables

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  18. caffeinemachine

    MHB A Conjecture About Polynomials in Two Variables

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  19. D

    MHB Infinite domain to finite plate by a change of variables

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  20. B

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  21. R

    MHB Solving xu_t + uu_x = 0: Need Help with Change of Variables

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  22. G

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  23. M

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  24. K

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  25. Zafa Pi

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  26. D

    MHB Limit of a vector of two variables

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  27. B

    Differential Equation: Separation of Variables

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  28. B

    Reformulating a simple cost function - combining 2 variables

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  29. H

    Deriving with multiple variables

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  30. C

    MHB Exponents - Numbers with Variables

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  31. J

    Need Some Mathematical Guidance Regarding Random Variables

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  32. F

    Mechanics, rewrite and solve equation, change of variables.

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  33. 5

    How are Entropy and Temperature conjugate variables?

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  34. S

    Maxima and Minima of a function of several variables

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  35. C

    Varying Variables and Differentials in Calculus Made Easy

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  36. L

    Transformations of variables support set

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  37. alyafey22

    MHB Creating a Summation Expression with k and m Variables

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  38. C

    Derivatives of functions of products of variables

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  39. J

    Expected Value of dependent random Variables

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  40. karush

    MHB A linear equation in 3 variables

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  41. I

    Change of variables in conditional pdf

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  42. E

    Are random variables based on the same pmf or pdf always independent?

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  43. S

    Fundamental Theorem of Calculus - Variables x and t

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  44. Mathelogician

    MHB Question on substitution of variables in natural deduction of predicate logic.

    Hi all, I need Explanation on the attached image from Van Dalen's Logic and Structure; specially on how the red part follows from the lines before it! Regards.
  45. S

    Solving Partial Differential Equations Using Separation of Variables

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  46. tsuwal

    Calculate integral through a change of variables

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  47. trash

    Convergence of random variables.

    Homework Statement Given a sequence of independent random variables {X_n}, each one with distribution Exp(1). Show that Y_n = \displaystyle\frac{X_n}{\log(n)} with n \geq 2 converges to 0 in probability but it doesn't coverges almost surely to 0. Homework Equations Density for each X_n...
  48. B

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  49. Mathelogician

    MHB A question on "Change of bound variables" Theorem (predicate logic)

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  50. M

    MATLAB Matlab fails to access a list of variables

    So I have a list of variables, defined in my workspace, and I'm trying to access them each in turn to compare them to a larger matrix A. The eval function calls each variable in turn, stores it under temporary matrix B, then compares it to matrix A, does the necessary calculation, and stores it...
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