Free Variables and Bound Variables - Examples

Examples

Before stating a precise definition of free variable and bound variable, the following are some examples that perhaps make these two concepts clearer than the definition would:

In the expression

n is a free variable and k is a bound variable; consequently the value of this expression depends on the value of n, but there is nothing called k on which it could depend.

In the expression

y is a free variable and x is a bound variable; consequently the value of this expression depends on the value of y, but there is nothing called x on which it could depend.

In the expression

x is a free variable and h is a bound variable; consequently the value of this expression depends on the value of x, but there is nothing called h on which it could depend.

In the expression

z is a free variable and x and y are bound variables; consequently the logical value of this expression depends on the value of z, but there is nothing called x or y on which it could depend.

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