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-- Recursive Functions over Reals, Differential Recursion, Concrete Sets (http://forum.wolframscience.com/showthread.php?threadid=1687)

Recursive Functions over Reals, Differential Recursion, Concrete Sets

Classical recursion is based on natural numbers. (step 1, step 2, step 3 ...) What if it was based on real or complex numbers? See subject for other ideas. What if there were Recursive Calculus, where the size of the step approached 0?

If a concrete set A were measured at 2 points in time, would the difference between A(t1) and A(t2) be the null set? Say I had a collection of 10 baseballs. Wouldn't the set of baseballs change in some way between the two measurements in time, making them unequal sets? If I have 2 distinct observers measure the same concrete set A at the same time, won't they see two different things? Isn't it true that you can never see the same rainbow twice?

Parallel Steps

I think the point is, that everything goes on in parallel. Only small thinkers think of things going on one step at a time.