General form of functions Is there a general form for functions? For example if the function is a polynomial, the general form is well-known. But is there a general one, covering every possible function?

To give a bit more detail about Michael Hardy's point:
Suppose a "description" or "form" of a function consists of a finite string of symbols chosen from a finite alphabet. Then it turns out that the set of all descriptions is countable (essentially, each can be seen as representing a natural number in some base).
Let $S$ be a set with at least two elements, and let $T$ be an infinite set. Then $S^T$ will have a cardinality of at least $|2^{\aleph_0}|$, the cardinality of the set of infinite bit strings. Cantor's diagonal argument shows this to be uncountable. So there isn't even any way to describe all functions from the set $\Bbb N$ to the set $\{0,1\}$, let alone something more interesting like the functions from the reals to the reals!
