# Dummy variable

1. Nov 11, 2005

### asdf1

can someone explain what's a dummy variable?

2. Nov 12, 2005

### mathwonk

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.

3. Nov 12, 2005

### sruthisupriya

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.

4. Nov 13, 2005

### asdf1

thank you very much!!!

5. Nov 13, 2005

### mathwonk

actually now i myself am puzzled by it, since by my definition, all variables are dummies!

6. Nov 18, 2005

### Don Aman

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: Nov 18, 2005
7. Nov 19, 2005

### mathwonk

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.

8. Nov 19, 2005

### Don Aman

Yup, that's pretty much it.