What is Variables: Definition and 1000 Discussions

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. H

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  2. M

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  4. H

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  5. P

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  6. P

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  7. P

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  8. G

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  9. O

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

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  10. R

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  11. J

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  12. M

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  13. J

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  14. Y

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  15. M

    Solving a PDE by Separation of Variables - Troubling Condition

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  16. J

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  17. Mandelbroth

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  18. S

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  19. J

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  20. J

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  21. H

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  22. E

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  23. K

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  24. fluidistic

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  25. D

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  28. H

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  29. P

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  30. A

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  31. D

    Force Equations: All Variables Given in Pictorial Form

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  32. M

    Mathematica Defining 2x2 Matrices with Variables for Solving DEs

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  33. D

    Everyday analogy why hidden variables can’t explain entanglement

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  34. 6

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  35. W

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  36. chisigma

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  37. T

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  38. E

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  39. P

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  40. A

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  41. M

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  42. C

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  43. N

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  44. S

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  45. C

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  46. B

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  47. H

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  48. D

    MHB Change of variables in a function

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  49. N

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  50. G

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