Re: Temporal database - no end date

[Sets without characteristic functions] What are those sets?

1. Fractals in which you cannot determine if a point x is on the curve or not.
2. A set defined by Collatz's "3n+1 conjecture". Start with an integer (n) run this procedure on it

WHILE (n <> 1)
DO IF odd(n) THEN n := 3n+1 ELSE n:= n/2;

Try it with 27 to see how long one of these things can run. The even numbers all reduce to 1 by inspection. But nobody has yet proved that all the odd numbers also reduce to 1. "The Dynamical System Generated by the 3n+1 Function" Lecture Notes in Mathematics" by Gunther J. Wirsching, (Springer Verlag, 1999) is a good place to start.

3) Any set defined by Godel's proof that you will have true theorems in a system complex enough to model arithmetic which cannot be proven true within that system.

There are tons more of these things. But that is really a topic for a Math newsgroup. Received on Sat Jan 20 2007 - 20:53:58 CET