MHB Introduction to linear algebra

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The discussion centers on proving that u(z+zw) equals the set {+1, -1, +w, -w, +w^2, -w^2}. Participants express skepticism about the proof's validity, likening it to absurd hypothetical scenarios. There is a call for clarification regarding the definition of "u" in the context of the problem. The conversation highlights the need for more information to approach the proof effectively. Overall, the participants seek a deeper understanding of the mathematical concepts involved.
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prove that u(z+zw)={+1,-1,+w,-w,+w^2,-w^2}
 
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abs said:
prove that u(z+zw)={+1,-1,+w,-w,+w^2,-w^2}

You may as well ask us to prove that if the sky is green then faeces smell like roses...
 
Prove It said:
You may as well ask us to prove that if the sky is green then faeces smell like roses...

If the sky is green, then a storm is coming.
If the storm comes, many things will be blown away, including faeces and roses. This, in turn, makes their smells mixed up.

Sorry, couldn't resist.
 
abs said:
prove that u(z+zw)={+1,-1,+w,-w,+w^2,-w^2}
Seriously, there must be more to this problem. What are you told about "u"?
 

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I have been insisting to my statistics students that for probabilities, the rule is the number of significant figures is the number of digits past the leading zeros or leading nines. For example to give 4 significant figures for a probability: 0.000001234 and 0.99999991234 are the correct number of decimal places. That way the complementary probability can also be given to the same significant figures ( 0.999998766 and 0.00000008766 respectively). More generally if you have a value that...
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