Math, asked by kanishksharma1234567, 1 month ago

Can you prove the Collatz Conjecture false?

Answers

Answered by AaravChhabra3008
0

The conjecture is named after Lothar Collatz, who introduced the idea in 1937. Since then, it has remained unsolved with its truth not yet verified. ... The company has chosen the Collatz conjecture because it thought many people can be easily interested in the problem, which itself is easy to understand

As of 2020, the conjecture has been checked by computer for all starting values up to 2^68 ≈ 2.95×10^20. All initial values tested so far eventually end in the repeating cycle (4; 2; 1) of period 3.

You will be tempted. This problem is simply stated, easily understood, and all too inviting. Just pick a number, any number: If the number is even, cut it in half; if it’s odd, triple it and add 1. Take that new number and repeat the process, again and again. If you keep this up, you’ll eventually get stuck in a loop. At least, that’s what we think will happen.

Take 10 for example: 10 is even, so we cut it in half to get 5. Since 5 is odd, we triple it and add 1. Now we have 16, which is even, so we halve it to get 8, then halve that to get 4, then halve it again to get 2, and once more to get 1. Since 1 is odd, we triple it and add 1. Now we’re back at 4, and we know where this goes: 4 goes to 2 which goes to 1 which goes to 4, and so on. We’re stuck in a loop.

Or try 11: It’s odd, so we triple it and add 1. Now we have 34, which is even, so we halve it to get 17, triple that and add 1 to get 52, halve that to get 26 and again to get 13, triple that and add 1 to get 40, halve that to get 20, then 10, then 5, triple that and add 1 to get 16, and halve that to get 8, then 4, 2 and 1. And we’re stuck in the loop again.

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