Kaon
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- Mar 12, 2018
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Sorry, I have to disagree. And it should be quite simple.
If you ask for a mathematical object with a magnitude of 4, then there is a multitude of potention solutions. As you said: no "unique" solution, but "working" (correct) solutions. Solutions that do indeed work for every possible situation.
But if you add further restrictions - like, vectors with a magnitude of 4... then a part of these previous solutions do not work.
Yet, in the question of our discussion... we have a solution that DOES work.
If you change your set of restrictions, so that this solution is excluded... you would have to justify your restrictions.
And as far as I understood it... you do not even exclude the "standard solution". You accept that it is a valid answer to the question... you just want to limit the question. But you won't say to what or for what reason.
I can only repeat: I don't know if you are on the right way with that or not. I may or may not have the necessary knowledge to understant that... but your not telling doesn't make it any easier.
If you don't want to present your reasons for your argumentation - for whatever personal reasons - maybe you should retreat from this discussion.
I am telling you exactly what the reasoning and rationale is. I don't think you don't have the background (you know enough about linear independence to recognize the requirement for bases). I think you may be ignorant - choosing to ignore, or ignoring by consequence very subtle details that make something go from infinitely possible, finite, and ultimately unique.
The restrictions I place on these problems are meant to highlight the restrictions in parameters we must meet in order to satisfy parts or all of a problem. I wish to find the unique solution; by consequence this solution will be highly restricted (otherwise, we would have a solution set).
My problem was made up by me to highlight the importance of uniqueness. The restrictions mimic the restrictions we see in nature (i.e. gravity doesn't act sideways, electric field does not curl around a source point charge). These are consequences of boundary conditions - the math - and allow us to determine unique solutions to problems (and, ultimately physics, chemistry and biology).
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