Let f(x) be a function defined on the positive integers such that:
f(x) = x/2 if x is even
f(x) = (3*x+1)/2 if x is odd
The conjecture is that iterates of f(x) will eventually reach 1 for any
initial value of x. Can anyone prove or disprove this?
2007-02-20 18:49:37 · 3 answers · asked by Shakespeare, William 4 in Science & Mathematics ➔ Mathematics
Hehehe. That conjecture has been around for a *long* time. But to date (so far as I know) nobody has shown an example that fails to converge to 1 after enough iterations. OTOH, nobody has proven that it always converges (after enough iterations) for all initial values of x. IIRC, there also several slightly different definitions for f(x). It's kinda in the same limbo as Goldbach's Conjecture, the 'twin-prime' question, and where Fermat's last theorem was until Wiles published his proof.
On a more positive note, it doesn't appear to be Gödel undecidable ☺
Doug
2007-02-20 19:13:10 · answer #1 · answered by doug_donaghue 7 · 1⤊ 0⤋
Me, no. Though neither can anyone else... yet. This is called the Collatz Conjecture and is as yet unproven either way.
2007-02-21 02:57:00 · answer #2 · answered by Phineas Bogg 6 · 1⤊ 1⤋
WHOA that is soooo hard. And no i cant solve it im only 13 years old
2007-02-21 02:59:28 · answer #3 · answered by chinas_chibi 1 · 1⤊ 0⤋