Writing from a phone, so please excuse any poor formatting.

So obviously with the Collatz conjecture all odd numbers don't need to be checked.

That being said would it be just as hard to prove that over time all numbers put through the function have a tendency to decrease in size? I mean obviously proving a tendency doesn't prove the conjecture but if it can be shown that the numbers will always eventually decrease it would be a way to build to the proof. Since we know the first large chunk are guaranteed to go to one by brute force.

Obviously, I'm probably stating the obvious here since I'm new to the problem, but it seems like you just need to show all numbers will eventually decrease. Which is probably much harder than expected.

Perhaps this is because you can only ever have one increase in a row

Ie 3n+1 Ã— will always end in a positive integer which will than be divided by two.

So as such you're very likely to get multiple even numbers in a row and decrease it quicker than it increases since you can only get one odd number at a time.

Or in other words you have to show that all numbers will have more even numbers decreasing the number than odd numbers can consistently increase it.

I guess that's probably just as hard to show though.

Just a thought journal lmao.

So obviously with the Collatz conjecture all odd numbers don't need to be checked.

That being said would it be just as hard to prove that over time all numbers put through the function have a tendency to decrease in size? I mean obviously proving a tendency doesn't prove the conjecture but if it can be shown that the numbers will always eventually decrease it would be a way to build to the proof. Since we know the first large chunk are guaranteed to go to one by brute force.

Obviously, I'm probably stating the obvious here since I'm new to the problem, but it seems like you just need to show all numbers will eventually decrease. Which is probably much harder than expected.

Perhaps this is because you can only ever have one increase in a row

Ie 3n+1 Ã— will always end in a positive integer which will than be divided by two.

So as such you're very likely to get multiple even numbers in a row and decrease it quicker than it increases since you can only get one odd number at a time.

Or in other words you have to show that all numbers will have more even numbers decreasing the number than odd numbers can consistently increase it.

I guess that's probably just as hard to show though.

Just a thought journal lmao.

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