What Are Dummy Variables and How Are They Used?

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Discussion Overview

The discussion revolves around the concept of dummy variables, exploring their definitions, roles in mathematical contexts, and implications in logic. Participants engage in clarifying the nature of dummy variables, their relationship to other types of variables, and the distinctions between bound and free variables.

Discussion Character

  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants define a dummy variable as one that acts as a placeholder in calculations and disappears in the final result, often taking values of 0 and 1 in statistics.
  • Others argue that all variables could be considered dummy variables since they can be replaced without changing the meaning in certain contexts, leading to confusion about the definition.
  • A participant introduces the idea that formulas without free variables are known as sentences in mathematical logic, which can be translated into English, while those with free variables cannot be assigned a truth value without context.
  • There is a suggestion that dummy variables are essentially bound variables, and that meaningful sentences in mathematics require all variables to be bound.
  • Some participants express uncertainty about the definitions and implications of dummy variables, indicating that the discussion is not settled.

Areas of Agreement / Disagreement

Participants express differing views on the nature and definition of dummy variables, with no consensus reached on a singular definition. The discussion includes both agreement on certain aspects and significant disagreement regarding the implications of variable binding and truth values.

Contextual Notes

Participants highlight the complexity of distinguishing between bound and free variables, and the implications this has for understanding dummy variables. The discussion reveals limitations in definitions and the need for clarity in mathematical logic.

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can someone explain what's a dummy variable?
 
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it is a variable which occurs with a quantifier, so that its role could be played by any other symbol.

e.g. in the definite integral of f(x)dx, from x = a to x =b, x is a dummy variable, since it could be everywhere replaced by any other letter and the meaning would be unchanged.or in the sentence, for every x between 1 and 2, x^2 lies between 1 and 4, we could replace all occurrences of x by any other letter and the meaning would be the same.
 
A variable that appears in a calculation only as a placeholder and which disappears completely in the final result is called a dummy variable.it usually takes on the values 0 and 1 (in statistics), and so can be called a binary variable too. In integration we use dummy variables.you know, the variables that are integrated out at the end of the problem.
 
thank you very much!
 
actually now i myself am puzzled by it, since by my definition, all variables are dummies!
 
mathwonk said:
actually now i myself am puzzled by it, since by my definition, all variables are dummies!
formulas in which no variable occurs free are known as sentences in mathematical logic. It is claimed that only sentences translate into English, while wffs with free variables do not. You can still give it a try though:
Ax x>y
would translate to
every number is greater than y. You can't say: every number is greater than some other number, because that has an implied quantifier.
You see free variables in elementary math a lot in contexts like f(x)=x^2, in which x appears to be free. But what is actually meant in that context is f: x|-->x^2, in which x is bound.
So your basic observation is that all variables are dummies is basically true: any meaningful sentence has no free variables. wffs with free variables are basically just used as building blocks for sentences.

And sentences have a better notion of truth, formulas with free variables can only be said to be said to be true relative to some assignment of the variables. For example, you cannot say whether the equation x^n+y^n=z^n is true or not. The best you can say is whether it's true relative to some assignment of the variables. On the other hand, the sentence "for some n greater than 2, there exists integers x, y and z, such that x^n+y^n=z^n" can be said to be true or false. It has only bound variables. Anything which can have an unambiguous numerical or boolean value has to have only bound variables.
 
Last edited:
so dummy variables are bound variables, and all variables in a meaningful sentence are bound.

e.g. an expression with an unboiund variable is like the english "sentence" : "he went to town." no truth value since no antecedent.
 
mathwonk said:
so dummy variables are bound variables, and all variables in a meaningful sentence are bound.

e.g. an expression with an unboiund variable is like the english "sentence" : "he went to town." no truth value since no antecedent.
Yup, that's pretty much it.
 

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