lime wrote:The function f(x) must be constructed just by "substituting" "x" instead of "n" in formula for f(n). Not in the arbitrary way as you did.
Are you saying that the domain of function f(x) must be the set of natural numbers?
If f : R -> R then why can't it be true that An = f(n) for all natural numbers n but f(n) = a constant value for all real numbers that are not natural numbers?
*It is not stated that (An) = f(n) only for all natural numbers n. If I assume it is only true for all natural numbers n, then I am right?