Talk:Free variables and bound variables

Is this article absurdly overspecialized, or what?

In the expression

$\sum _{x=1}^{10}f(x,y)$

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

$\sum _{y=1}^{10}f(x,y)$

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

In the expression

$\int _{0}^{\infty }x^{y-1}e^{-x}\,dx$

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

$\lim _{h\rightarrow 0}{\frac {f(x+h)-f(x)}{h}}$

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

$\forall x\ \exists y\ \varphi (x,y,z)$

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

Michael Hardy 00:09 Feb 20, 2003 (UTC)

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