rodgers madden rating is gonna drop too low for woody johnson’s liking
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Pick a positive integer n. If it is even, divide it by 2. If it is odd, multiply by 3 and add 1. Then, repeat this operation with the result. Is there any n such that if you repeat the operation above an infinite number of times, you will never reach the number 1?
- Yes (please share which number)
- No (please provide a proof)
0 voters
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yeah give me a second i’m running through all the possibilities
it should only take a few years provided my hardware doesn’t crash
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my computer crashed
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Wow no option for undecidable? Rigged. What would Gödel think?
where was this OSU against Michigan lmao
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they can still lose
surely
if they blow 34-0 ryan day will see a firing squad
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There is no such number
By dividing an even number to 2, we are not necessarily turning it into odd. It could still be even. And we can divide again and again. We can combo
By doing the other step, multiply an odd number by 3 and add 1, we are turning an odd number into even. We can only do this once at a time. We cant combo
We end up dividing more often than not. Although im not sure how to prove that
I played it out with some random numbers in my head and it always works out. The fact that you can combo divide multiple times in a row means you just end up decreasing the value way more than youre increasing it
I dont know the correct way to prove it though. If this isnt sufficient enough
For such a number to exist, you must not be able to combo divide it. Which means you cant end up dividing it by 4. Its difficult to end up with a number like that i think if you infinitely transform the number with these steps, from odd to even and vice versa
If i can find a number that when its even in the loop it only gets divisable by 2 and never by 4 that proves the main thing too, thats the n. And if i can prove theres no such number that proves theres no such number for the main thing too, no n exists. But i dont know how
WAIt i think i got it
You solved the Collatz conjecture?
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DM me the proof and don’t show it to anybody else ok?
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Lets say X is our number before we do the last possible division by 2. X is guaranteed to be even
We are now working with X/2. X/2 is now an odd number. We move to step two
We get 3/2*X + 1
This number is guaranteed to be even
We can transform that to (3X + 2)/2
This number is always divisable by 4 (is my claim)
Because its even, thats the first 2
And then …
Can I prove (3X + 2)/4 is always an even number thats at least 2
Uhhh
X is guaranteed to be even from how i defined it. So 3X will always be even. And adding 2 is also an even number. It stays even. Dividing by 4 … I mean it cant go to 1 coz X needs to be at least 2. So the end result of that is always 2 at least. So we will always be able to eventually delete it by 4, and thus combo delete
It made sense in my head but from what youre saying i gather nobody has managed to prove it. Damn 
. Where. Did i go wrong in my attempt? Im so curious
who up mounting they eerie
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proving that you can divide by 2 multiple times in a row isn’t sufficient though
you haven’t shown your number doesn’t get large again later
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if he believes it whos to say it doesn’t
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