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. S

    What is the median value of an odd-numbered set of letters?

    I wonder what parts of statistics have specific terms existing for them - I see a relevant notion which would be relevant, but not sure if there is a term for it. If variable values can be ordered then it possesses a median. If the values can also be added then they also possesses an average. A...
  2. N

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  3. A

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  4. M

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  5. MarkFL

    MHB Find x,y Coordinates of Stationary Point: 2x^2-2xy+y^2+2x+5

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  6. N

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  7. L

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  8. binbagsss

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  9. Y

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  10. M

    Cannot work out change of variables in Integral

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  11. Y

    Which one could be the three confounding variables?

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  12. N

    Can Constants with Variables Cancel Out to Create a Constant?

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  13. M

    How do I calculate this double integral using a change of variables?

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  14. P

    Sum of two independent uniform random variables

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  15. C

    Change of variables in a differential equation in Maple

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  16. L

    MHB Solving Variables Puzzle: Correlation Coefficients & SPSS for N=850

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  17. O

    Challenge 8: Sub-Gaussian Variables

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  18. F

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  19. MarkFL

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  20. S

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  21. C

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  22. F

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  23. S

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  24. M

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  25. S

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  26. T

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  27. F

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  28. E

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  29. S

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  30. P

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  31. C

    Integrationg over exp with two variables

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  32. P

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  33. Petrus

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  34. S

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  35. H

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  36. D

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  37. K

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  38. L

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  39. I

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  40. B

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  41. B

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  42. S

    Fortran [Fortran 90] Output is NaN in variables

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  43. B

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  44. E

    MHB Partial DE-separation of variables

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  45. E

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  46. E

    Complex Variables: Area Enclosed by Contour Formula

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  47. R

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  48. O

    MHB Joint cumulative distribution of dependent variables

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  49. R

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  50. F

    MHB Solve by separation of variables

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