The Collatz Conjecture: Impossible?
My analysis and theoretical conclusion
Let’s take a brief look at what this puzzling Collatz Conjecture is.
This conjecture involves a sequence of numbers with 2 simple rules attached to them:
x = number
If the number is even, divide the number by 2, or (x/2)
If the number is odd, multiply the number by 3 and add 1, or (3x +1)
The idea is that no matter what number you start with, using these rules you will always end up at 1. People have been trying to prove this wrong for a long time since it was introduced by Lothar Collatz in 1937, but unfortunately, no one has succeeded.
Today, I will propose my theory.
This is an example, starting with the number 7:
7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1
As you can see, the sequence ended up at 1, as expected.
I strongly believe that the most reasonable solution to the Collatz Conjecture is infinity (∞)
The laws of addition and multiplication you are using hold for natural numbers, but ∞ is not a natural number, so these laws do not apply. These are laws such as a number multiplied by 0 is always 0.
As such, anything multiplied by ∞ has to be ∞, no matter how small or how large the number is.
Addition is basically repeated addition, so adding anything to infinity isn’t possible either. The answer will remain ∞.
Since division is the opposite of multiplication, the same rules apply for it. Hence, anything divided by ∞ is still ∞.
Recap: ∞ times anything is ∞. ∞ divided by anything is also always ∞. Lastly, anything added to ∞ is also still ∞. If this is not true, then ∞ can’t be possible.
Even though ∞ is considered a concept, a concept can still be the solution to conjecture. There is no need for an exact number. For incomplete information, we can have an answer that makes the most sense.
Every positive number has one of two qualities: odd or even. There isn’t a single number, according to our current knowledge, that is unique in a way that it could answer to something so complicated, such as this conjecture.
We can try using 30 computers going through each number to see if it doesn’t end up at one. It will never work. Ever.
If you want to try this yourself, please check out this very simple python program by Michał Szmigiel on the Collatz Conjecture. Try it yourself!
Stay safe everyone!
