Firemorphic
Activist Membrane
The entire frame-of-reference of the question is invalid.
This is true so many time over, worth a million 'winner's.
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The entire frame-of-reference of the question is invalid.
The Collatz conjecture is a conjecture in mathematics that concerns a sequence defined as follows: start with any positive integer n. Then each term is obtained from the previous term as follows: if the previous term is even, the next term is one half the previous term. If the previous term is odd, the next term is 3 times the previous term plus 1. The conjecture is that no matter what value of n, the sequence will always reach 1.
The Challenge: Pray to your God for a proof/disproof of the conjecture. Post the proof/disproof here. If your god gives you a valid proof/disproof, I will believe in your god and convert to your religion.
God does not work that way. No one else can pray for proof for you or proof that would convince you. If you want proof you must seek God yourself, there is no go between. God desires a relationship with you personally and that you would seek Him directly to know of His existence or presence.
The Collatz conjecture is a conjecture in mathematics that concerns a sequence defined as follows: start with any positive integer n. Then each term is obtained from the previous term as follows: if the previous term is even, the next term is one half the previous term. If the previous term is odd, the next term is 3 times the previous term plus 1. The conjecture is that no matter what value of n, the sequence will always reach 1.
The Challenge: Pray to your God for a proof/disproof of the conjecture. Post the proof/disproof here. If your god gives you a valid proof/disproof, I will believe in your god and convert to your religion.
There was a short story many years ago about a mathematician that agreed to sell his soul to the devil if he would get a proof of Fermat's Last Theorem within 24 hours in return (this was well before 1994 when it was finally solved after 358 years).
The story mostly deals with the devil learning the different types of math that had been used to attack the problem up to that time. Ultimately, the time ran out and the devil had to admit defeat.
The last line was the devil saying he had an idea to try next.....
The Collatzs conjecture isn't as sexy as FLT was, but you might get a better bargain with someone who makes deals....
/E: Found it: "The Devil and Simon Flagg" by Arthur Porges.
I'd also point out that a generalization of the Collatz conjecture is known to be undecidable. In essence, there is no computer program that will determine from the input (integer n, and iteration function) whether the sequence will reach 1.
Collatz conjecture - Wikipedia
So, it is *possible* that this conjecture is unsolvable: there is simply no way to determine if this process stops for every integer or not.
The Collatz conjecture is a conjecture in mathematics that concerns a sequence defined as follows: start with any positive integer n. Then each term is obtained from the previous term as follows: if the previous term is even, the next term is one half the previous term. If the previous term is odd, the next term is 3 times the previous term plus 1. The conjecture is that no matter what value of n, the sequence will always reach 1.
The Challenge: Pray to your God for a proof/disproof of the conjecture. Post the proof/disproof here. If your god gives you a valid proof/disproof, I will believe in your god and convert to your religion.
It seems that this iterative algorithm is one that "finds" a certain series of numbers, which is the series of all numbers that can be expressed as 2 to the power of n. Once it finds a number in that series the algorithm iterates until it reaches 1 by the condition for even numbers. Then it stays in a cycle of 1 4 2 1...
The way it finds that series is to make all odd numbers even and larger is a minimal but non-trivial way. It is, in effect, a random number generator that repeats until it lands on the 2 to the power of n series.
I think that the trick might be to show that for this algorithm that the iterations never fall into a repeating loop other than the one which ends as above.
I will give it some more thought...
It seems that this iterative algorithm is one that "finds" a certain series of numbers, which is the series of all numbers that can be expressed as 2 to the power of n. Once it finds a number in that series the algorithm iterates until it reaches 1 by the condition for even numbers. Then it stays in a cycle of 1 4 2 1...
The way it finds that series is to make all odd numbers even and larger is a minimal but non-trivial way. It is, in effect, a random number generator that repeats until it lands on the 2 to the power of n series.
I think that the trick might be to show that for this algorithm that the iterations never fall into a repeating loop other than the one which ends as above.
I will give it some more thought...
My understanding of the conjecture is that it is logically equivalent to (by generating possible previous terms) starting with the number n equals 8 and multiplying by 2, then if the next generated number is congruent /equivalent to 4 mod 6, two new numbers are generated, namely (n-1)/3 and 2n, or if the next generated previous number is not equivalent to 4 mod 6, only one number is generated, namely 2n. The question is whether the set of all positive integers can be generated in this fashion starting with 8. This is a "backwards" way of looking at the conjecture, and I probably didn't do a great job of explaining it, but am I correct in thinking this is an equivalent question?
Why would He drop all that and dance to your tune?
God does not work that way. No one else can pray for proof for you or proof that would convince you. If you want proof you must seek God yourself, there is no go between. God desires a relationship with you personally and that you would seek Him directly to know of His existence or presence.
Right...your whole tone and attitude is one of sarcasm and if I can pick up on that certainly God knows you are not sincere.
The challenge is of the God as a piñata that we can "whack" with prayers and who gives out goodies, in this case proof. The entire frame-of-reference of the question is invalid.
The Collatz conjecture is a conjecture in mathematics that concerns a sequence defined as follows: start with any positive integer n. Then each term is obtained from the previous term as follows: if the previous term is even, the next term is one half the previous term. If the previous term is odd, the next term is 3 times the previous term plus 1. The conjecture is that no matter what value of n, the sequence will always reach 1.
The Challenge: Pray to your God for a proof/disproof of the conjecture. Post the proof/disproof here. If your god gives you a valid proof/disproof, I will believe in your god and convert to your religion.
This is true so many time over, worth a million 'winner's.