OH BOY OH BOY I GET TO EXPLAIN 3X + 1
So just β3x +1β³ is an expression, not an equation, however itβs also shorthand for an infamous mathematical problem known as the βCollatz Conjectureβ. Itβs a very, very, VERY simple question that still has mathematicians scratching their heads.
The premise goes like this:
Take a number (a positive integer) and call it βxβ.
If that number is even, divide it by 2. If the number is odd, then multiply it by 3 and then add 1 (3x + 1). Repeat over and over again. (so you could go 3, 3(3) + 1 = 10, 10/2 = 5, 3(5) + 1 = 16, etc.)
The Collatz Conjecture (aka the 3x + 1 problem) states that eventually, this sequence will always lead you to the number 1 where it loops 1=>4=>2=>1=>4=>2=>1=>4=>2=>1 forever, regardless of which number you start this sequence with.
Now, there is no proof that this is true or false yet (hence the βconjectureβ part).
If you want to disprove the 3x + 1 problem, all that you have to do is find a positive integer that does not ever make it to 1, either by finding a closed loop of numbers that ISNT 1=>4=>2=>1 or by finding a value that just has it keep increasing to infinity (7=>22=>11=>34=>17=>52=>27=>82=>41=>122β¦..while this sequence does end up coming back down to 1, people theorize there could be a starting point where it just keeps going up and up and up forever). If you can just find ONE, then you will have successfully solved 3x + 1.
But to this day, every single positive integer has been tested from 1 to 2^68 (or approx. 1-300,000,000,000,000,000,000 (300 quintillion). None of them have proven to be an exception.
But any Cookie Clicker veteran knows that 300 quintillion is childβs play. A number that makes an infinitesimal speck of dust look like a god damn multiverse in relation to infinity. And we donβt exist outside of time (yet) so we probably arenβt going to be able to test an infinite number of positive integers.
So if you want to prove the 3x + 1 problem, you gotta make a proof. If youβve never done mathematical proofs before or donβt know what they are, remember back in school when your teacher gave you those βSolve for x:β questions and you had to move numbers and variables around until you got the right answer? Yeah, you gotta do that. A lot. And you MIIIIIGHT be able to get to the right answer. That triple dot thing from Beginnerβs Guide shows up there although itβs upside down apologies I am very tired, and like the Beginnerβs Guide, crying once or twice is completely normal and even expected.
But no one has been able to make a proof yet. So there 3x + 1 stands to this day. The most deceptively simple math question that has stumped mathematicians for decades. If you want a more in-depth talk about this problem, this video does a fantastic job going into the details.
Thanks for giving me the chance to talk about math!!!!!
