While that maybe true in general, let me worry about other underlining issues for the time being because answering this particular question also helps me understand what can and can not be done using pure functions in Mathematica. Right now, my principle goal is to get code that produces my desired results, followed by learning more programming strategies, followed by the efficiency of the code. If it helps, the topology of the space I'm working in is important, not the metric (I'm free to use any yardstick I wish).
If the only way to get the result I desire is to explicitly declare a variable "s", please say so.
And Rohit, I'm trying to be polite but it is getting difficult as I find it extremely offensive when people try to second guess me. I appreciate the help but please answer the question asked.
