This is what I had initially thought of as the definition but immediately threw it away because it was not commutative. I guess I should never assume such things.
Also I am still curious if anyone knows a definition that works in any vector space.
I was discussing with a friend of mine whether the zero vector is parallel to all other vectors. We came to the conclusion that it probably is but we do not know the formal definition of parallel.
What is the formal definition of parallel? Wolfram says that two vectors are parallel iff their...
Yeah i wish I could dot dot dot this one but that's definitely not allowed. I reallized that I had messed up at an earlier part of this problem anyway. Thanks though.
@verty While what I said was not 100% rigourus I could easily make it that way.
For all natural numbers n, if x is not \geq n...
Well I feel a little bit guilty for even posting a homework question at all (It's cheeting). So I am not going to post specifics. I will clarify certain things if people have questions. I think that someone could figure this out with the information I have given. If not then I will just have to...
So I have to do an induction but I am not quite sure how to set it up. I have already proven that at each step I have either my intended result or I can advance one more step. I have also proven that there are a finite number of steps.
Intuitively I have essentially completed the proof. I...
I think that the problem here is a bad definition. Clearly when something is freefalling there is a force on it or it would not accelerate. There is no pressure despite this. It seems like in every example here the force is a normal force.
So I think the definition should be Normal...
Sorry I have ignored this thread that I started.
These ansers are not quite what I was looking for. The "problem" does not have to be an unexplained physical phenominon. I will explain what I mean with an example. Last year my friend asked his physics proffessor, "If you have two rods spinning...
Also I would consider what it means to say that M is the "only" minimal set with property P. To know this you would have to consider every set possible but the set of all sets does not exist.
Edit: I guess you could prove that the empty set is the only set with P = "has no elements".
Good point. I am pretty sure 0 is still going to be the best answer but I have to consider the problem more thoroughly.
Edit: The answer will probably be 0 assuming there is some sort of reasonable answer at all.
I don't know anything about stockfish so this might be irrellivant. Most android apps are written in java, which means the slowdown of running in a VM.
Yes it is important to write a lot of proofs for proactice. It is also, important, however to read a lot of proofs. Go to the library (preferably of a college if you can) and check out a book on algebra or set theory (or anything else). Just reading the proofs in the book will teach you farely...
Technically the set of all functions does not exist. It is to big to be a set.
If you mean real valued functions, while the above post is completely correct, I think the answer you want is f(x) = 0. If you sum every function, I believe you will get 0 because for every f(x) there exists g(x) = -f(x)
In Principia Mathematica, type theory is used, which is a very complicated set theory. In modern set theory it is quite easy to prove 1 + 1 = 2 as I showed in post 36. This is a formal proof like Russell's, except it uses the now standard ZFC axioms.Edit: I have not actually read Principia...
Are there any unanswered questions in classical mechanics?
By unanswered I mean unanswered and attempted. I could easily think of a question which has never been asked.
Edit: Sorry about the misspelled thread title.