Talk:Free variables and bound variables

Is this article absurdly overspecialized, or what?

The following examples should be incorporated into the article. I will probably do this, but I'd like to discuss how best to make it mesh with the somewhat more esoteric matter on the lambda calculus that is already here.

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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I have now incorporated all of those examples into the article. The transition from the list of examples to the proposed precise definition, which I suspect may be too narrow, is abrupt. The article needs polishing, by someone familiar with logic and with the lambda calculus. Michael Hardy 22:51 Feb 23, 2003 (UTC)