Why Collatz conjecture is a mystery?
What is Collatz Conjecture?
The Collatz Conjecture is a mathematical mystery. This problem is very simple to understand but the dynamic nature of the conjecture makes proving or disproving it very difficult. This difficult problem concerns a numerical sequence as follows. Start with any positive integer 'n' and that should not be 0. If 'n' is odd, perform '3n+1' and if it is even, perform 'n/2'. Perform this again and again with the answer and no matter what the value of 'n' is, the sequence will reach 4, 2, 1 forever. Conclusively, this conjecture states that, this number process will eventually reach at one which is called the stopping time of the number.
It is named after Lothar Collatz who introduced this idea in 1937, two years after his doctorate. He is a great German mathematician.
Why Collatz conjecture is a mystery?
Now the question arises, that, then why is it a mystery??? Many mathematicians claim that a counterexample for this conjecture also exists ( As many of the conjectures have). If this sequence is false, a counter cycle should be there which isn't founded yet. Due to such claims, it is a mystery. In many other conjectures, a counterexample is found by using very large numbers. This Collatz Conjecture has reached 1 million but no such number is found that would disprove the conjecture.
Let's try an example...
Let's start with 10.
10/2=5
3(5)+1=16
16/2=8
8/2=4
4/2=2
2/2=1
3(1)+1=4
4/2=2
2/2=1
And 4, 2, 1 will go on forever.
Posts before October 2021 have been marked as "Old Posts". Less likely, but they might have out dated or incorrect information, ugly looking bits of code, no labels, etc. Don't get me wrong, many of these posts are top-notch and interesting too.
I thought it would be better not to delete or revamp these posts, even if they suck. The bitter truth is that old works always suck, but I take that as a positive tool to convey that I am growing. Besides there's no better way to showcase my journey without these old, messy, poorly written posts!
I thought it would be better not to delete or revamp these posts, even if they suck. The bitter truth is that old works always suck, but I take that as a positive tool to convey that I am growing. Besides there's no better way to showcase my journey without these old, messy, poorly written posts!
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