Definition:Bound Variable

Definition
A dummy variable (or bound variable) is a variable which, when it occurs in an expression, can be replaced with another variable without changing the meaning of the statement.

Examples

 * See the definition of universal statement.

In the statement:
 * $$\forall x: P \left({x}\right)$$

the variable $$x$$ is a dummy variable.

Also see the definition of existential statement.


 * In algebra:
 * $$x^2 + 2 x y + y^2 = \left({x + y}\right)^2$$

Both $$x$$ and $$y$$ are dummy variables.