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From: Don.zed on 20 May 2010 10:24
From Wikipedia:

"The proof of the conjecture can indirectly be done by proving the following:

[A] no infinite divergent trajectory occurs
[B] no cycle occurs

thus all numbers have a trajectory down to 1."


Aren't A and B both cycles? Consider a state machine that describes the problem. Then clearly B means we are in some state, where x has some value, and we cycle within this machine until we eventually arrive back at the original state, where x again takes on its previous value. But in B, we must also cycle within this machine. The difference is that x never takes on its previous value, it just keeps cycling around growing larger and larger.
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