Your post purports to conclude: “That’s why [the Collatz conjecture] will never be solved”.
Do you think it would also be correct to say: “That’s why [the Steve conjecture] will never be solved”?
If yes, then I think you’re using the word “solved” in an extremely strange and misleading way.
If no, then you evidently messed up, because your argument does not rely on any property of the Collatz conjecture that is not equally true of the Steve conjecture.
Yeah, just went through this whole same line of evasion. Alright, the Collatz conjecture will never be “proved” in this restrictive sense—and neither will the Steve conjecture or the irrationality of √2—do we care? It may still be proved according to the ordinary meaning.
Look at other unsolved problems: - Goldbach: Can every even number of 1s be split into two prime clusters of 1s? - Twin Primes: Are there infinite pairs of prime clusters of 1s separated by two 1s? - Riemann: How are the prime clusters of 1s distributed?
For centuries, they resist. Why?
I think it would be much clearer to everyone if the OP said
Look at other unsolved problems: - Goldbach: Can every even number of 1s be split into two prime clusters of 1s? - Twin Primes: Are there infinite pairs of prime clusters of 1s separated by two 1s? - Riemann: How are the prime clusters of 1s distributed? - The claim that one odd number plus another odd number is always an even number: When we squash together two odd groups of 1s, do we get an even group of 1s? - The claim that √2 is irrational: Can 1s be divided by 1s, and squared, to get 1+1?
For centuries, they resist. Why?
I request that Alister Munday please make that change. It would save readers a lot of time and confusion … because the readers would immediately know not to waste their time reading on …
The Steve Conjecture still requires universal quantification—“For ALL positive integers, this process leads to 1.” That’s above pure arithmetic level.
In pure arithmetic we can only verify specific cases:
”1 is odd → 2 → 1“
”3 is odd → 4 → 2 → 1”
”5 is odd → 6 → 3 → 4 → 2 → 1″
To prove it works for ALL numbers requires stepping above arithmetic to use induction or other higher structures.
Your post purports to conclude: “That’s why [the Collatz conjecture] will never be solved”.
Do you think it would also be correct to say: “That’s why [the Steve conjecture] will never be solved”?
If yes, then I think you’re using the word “solved” in an extremely strange and misleading way.
If no, then you evidently messed up, because your argument does not rely on any property of the Collatz conjecture that is not equally true of the Steve conjecture.
Yeah, just went through this whole same line of evasion. Alright, the Collatz conjecture will never be “proved” in this restrictive sense—and neither will the Steve conjecture or the irrationality of √2—do we care? It may still be proved according to the ordinary meaning.
Yeah it’s super-misleading that the post says:
I think it would be much clearer to everyone if the OP said
I request that Alister Munday please make that change. It would save readers a lot of time and confusion … because the readers would immediately know not to waste their time reading on …