I am a noob at this stuff but I do enjoy watching numberphile videos. I caught the one about the Collatz Conjecture yesterday. At one point he demonstrates that while you are doing the operations for any number you may have picked, if you end up on a number that has been a starting point before which has been proven to go to 1, then you can stop right there and don't need to continue. This got me to thinking, if there were a number which defied the Collatz Conjecture, wouldn't that mean that every single number you get to when performing the operations on it (3n+1, /2 ) would ALSO have to defy the Collatz Conjecture? So if you take the magical number and do 3n+1 to it, whatever that number is would also have to not go to 1, and then if you divide that number by 2, that next number would also have to not go to 1. So on and so on.

Is this correct or am I missing something here?

Thanks,