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In honor of Pi Day (March 14), here’s a mathematical topic for you.
I know this isn’t likely for the non-mathematically inclined, but consider the following: Choose a positive integer (i. e. whole number). If it’s odd, multiply it by 3 and add 1. If it’s even divide it by 2. Then repeat this process on the result, and see where you end up.
Consider an example. I’ll start with 10: 10 is even so 10/2 = 5. 5 is odd, so 3x5 + 1 = 16. 16 is even so 16/2 = 8, which is also even. 8/2 = 4 (even), so 4/2 = 2, and 2/2 = 1.
It turns out that for that, as far as anyone knows, for any positive integer you pick, the result of this procedure will always end at 1. The procedure may take many, many steps, but it seems you always find yourself at 1, in the end. The Collatz conjecture states that any positive integer undergoing this process will always end at 1. However, despite much effort devoted to proving this conjecture, no one has found a proof. It may seem strange that such a simple mathematical process has resisted the force of some pretty knowledgeable mathematicians, but this sometimes happens. It has been proven, that, statistically, for a randomly chosen integer, the probability of getting 1 as an end result is 100 %, but that hides the possibility of a single integer, or a small number of integers, that violate the rule. If the conjecture is unprovable, it could either be wrong (meaning that there is a positive integer where this process will not end at 1), or it’s true but unprovable (meaning the tools used in mathematical proofs are just insufficient to prove it).
That’s all for tonight. Comments are below the fold.
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