Recent content by AllyScientific

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    Undergrad Getting i^3 = -i using laws of surds

    I suspect that the mathematicians themselves are starting with a false premise, because they are breaking the law of signs. Need I add that they are not infallible? They are breaking their own law, should I not have right to say it ? My point is that we should start with a right premise...
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    Undergrad Getting i^3 = -i using laws of surds

    -i is negative and +i is positive. (-i)*(-i) = (+i)*(+i) = i^2 =-1 Does it make sense now? A negative number \times a negative number = a negative number.
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    Undergrad Getting i^3 = -i using laws of surds

    I think Tobias is talking about my recent threads where I showed my resistance to the supposed fact that \sqrt{ab} = \sqrt{a} \sqrt{b} doesn't always hold. If it makes no sense that i is positive in i^2=-1, then i is negative. But does it make sense that a negative number \times a negative...
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    Undergrad Square roots of unity and the validity of √(xy) = √x√y

    If it is a mis-proof, it must be proved to be such, just saying it is does not make it a mis-proof. I am myself also trying to prove -1 = 1 false, if I can. We should abandon theology and aim to scientific methodology if possible. In that case, the only possibility is to study the problem...
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    Undergrad Square roots of unity and the validity of √(xy) = √x√y

    I don't think anyone can say for certain that proving true the statement 1=-1 will contain an error. It is only a priori hypothesis that the attempt is doomed to failure. It does not prevent someone from finding a proof some day, whatever the result of the proof will be. Of course what I have...
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    Undergrad Square roots of unity and the validity of √(xy) = √x√y

    I think a lot a users have vague concepts about the roots of unity. I try to post a link to WolframAlpha, which calculates all the second roots of unity http://www.wolframalpha.com/input/?i=sqrt%281%29 There you can see the input \sqrt{1} and the plot of all roots in the complex plane...
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    Undergrad Why does (-1) × (-1) = +1 if imaginary numbers obey different rules?

    I must ask you the same question as about ZeroPivot, did you read what I wrote? I have given a proof that Wikipedia is wrong about proving that √1 = -1 is a mathematical fallacy, while you assume that Wikipedia is correct. Do you know what are the roots of unity? Especially what is the second...
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    Undergrad Why does (-1) × (-1) = +1 if imaginary numbers obey different rules?

    It seems to me that you did not even read what I said. I have presented you a proof that: √1 = -1 and the proof is based on the concept of the roots of unity. Do your homework and learn what are the roots of unity. You will find that a second root of unity means the same as the square root of 1...
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    Undergrad Why does (-1) × (-1) = +1 if imaginary numbers obey different rules?

    I did a little research about the possibility of i being multivalued, because above is a formula where we can calculate that i=+1 and i=-1 besides the well known i=√-1 . This means that +1 = -1, and we seem to have made a mathematical fallacy if we trust Wikipedia which says that: +1=√1...
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    Undergrad Why does (-1) × (-1) = +1 if imaginary numbers obey different rules?

    There is the result (+i)^2 = (-i)^2 = ((-1)x(-1))x((i)x(i)) = (i)x(i) = (1)x(-1) = -1. → i= 1 and i= -1. It could be that there are the values i=1 and i=-1 besides the usual i=√-1, although this may sound a strange idea. At least the usual multiplication rules are then valid...
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    Undergrad Why does (-1) × (-1) = +1 if imaginary numbers obey different rules?

    If i is not a negative number, but a positive one ( also the same as +i), then -i is a negative number, and (-i)x(-i) = (+i)x(+i) = i^2 = -1 so we have the result: a negative number times a negative number equals a negative number. And yes, there appears to be a violation of the old rules.
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    Undergrad Why does (-1) × (-1) = +1 if imaginary numbers obey different rules?

    Marilyn vos Savant, who claims to be in the Guinness Hall of Fame for “World’s Highest IQ.”, has written the book The World’s Most Famous Math Problem, and here is a direct quote from the book, page 61: The square root of +1 is a real number because +1 × +1 = +1; however, the square root...