[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 560

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I am not clear, I will try to reformulate it.
)))
While writing the reformulation, I realized that we can simply leave M+1 dimensions in the original problem, just equating the other components of the required vector to zero. So, the problem should be reduced to N=M+1.
That's all, the question is solved, I'm going to restore brain activity))))
Imho, the problem has no solution, except for the trivial case when orthogonality of vectors in a space of dimension m unambiguously means that they are orthogonal in n>m space. By the way, the limiting case: m=0 (not m=1), in which case an orthogonal to the original coordinate system will be a vector located in any one-dimensional space including the original zero-dimensional space.
our case is exactly trivial. :) we observe the boundary conditions. including the zero-dimensional case. ;)
the problem is solved.
We have a trivial case. :) we observe the boundary conditions. including the zero-dimensional case. ;)
the problem is solved.
We have a trivial Cartesian space, and it's straight to the point of nausea. :)
Then, what result (Offtopic) do you expect?
I think it's time for bed :)
Good night.
Then, what outcome (Offtopic) are you hoping for?
Lots and lots and lots and lots of money and money and money...!!!!!........!!!!!!........$$$$$$$$$$$$$$$$$...................
;)
Lots and lots and lots and lots of money-money-money-money...!!!! ........!!!!!!........$$$$$$$$$$$$$$$$$...................
;)
Makes sense. What are we going to make money on?
How are we better than others?