"William Elliot" <email@example.com> wrote in message news://20020502045557.L86227firstname.lastname@example.org... > Start with a number n and repeat: > if n is even, then divide it by two > if n is odd, multiply it by 3 and add 1. > > Eventually n will > 1. reach 1 > 2. get bigger and bigger > 3. repeat an earlier value
Of course if 3 is true then 1 is untrue (other than the trivial case). If 2 is true then 1 is untrue. And conversely if 1 is true both 2 and 3 are untrue.
These three states incidentally match those of the solutions of first order differential equations -i.e. damping, oscillation and exponential growth. Or of couse if you like chaos theory there could be a solution which takes on an infinite set of (chaotic) values - or is this the same as getting bigger and bigger?