Ahh, thanks! That finally settles my question in the OP: indeed, propositions of existence (and therefore also propositions of non-existence) are special, because of that property called "Sigma-1 completeness", which is what I invoked unknowingly when I said to take the counterexample and check...
Thanks for clearing it up. Could you please point me to these theorems? I'd like to understand why the same can't be applied to "not Goldbach", i.e. by your sentence, if the proposition "Goldbach is false" is unprovable, then it's true, therefore Goldbach is false. Since it can't be both, there...
Thank you all for your replies.
This is right at the heart of my question.
So, if Goldbach's conjecture was indeed unprovable within Peano, and we add its negation to the axioms, what we would have is a finite natural number whose value can't be determined, that we can't write as an...
I was once told that Goldbach's conjecture could perhaps fall into Gödel's first incompleteness theorem, and be true but not provable. Is that really the case?
I mean, if Goldbach's conjecture were false it would be easily provable, as it would mean that an even number exists that is not the...
I just found a simple proof that my solution is not minimal, unless there are multiple minimal solutions, which I doubt: Rotating the reference system should give a rotated solution. It doesn't.
Yes, that's right.
I've been giving a bit more thinking to the (possibly not minimal) solution I've stated, namely to fix the maximum acceleration for both axes since the beginning. It seems to me that finding the maximum acceleration per axis that makes the times match, would be the...
lalbatros, thanks, but I'd have a hard time converting your explanations to something I could use. I'm convinced that the approach I've stated above must be really close to the optimal one, and I might end up using it. If you or someone can put the explanations in a more practical form, as K^2...
Yes, the destination point has to be reached at zero speed.
But your idea of a constant acceleration suggested me another approach.
It seems that finding a provably optimal solution is going to be really tough. I don't know if this solution is optimal, it probably isn't, but here we go. It...
Nobody has an answer? Is the problem really that tough? I also discussed it in IRC (FreeNode) for hours, and none of the people who tried could come up with an answer. It seems no piece of cake indeed.
An alternative formulation for the problem is: find a function a_{p_F, v_F}(t) that gives...
I have this problem.
Imagine, in 3D space, a rocket that has to go to a certain point in the minimum possible time, so that when it gets to its destination its speed is 0. How much thrust to apply and in what direction?
My problem is purely ideal: there is no mass loss due to fuel...