-1=1 ??
Created on: November 12th, 2006
A "proof" of how 1 = -1 by simple algebra using only the true statement i^2 = -1.

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November 12th, 2006
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its impossible tyo have a negative under a radical is it not?, i may just be stupid idk
November 12th, 2006
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nothing squared equals a negative number. a negative times itself, just like a positive times itself, is a positive number.
November 12th, 2006
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All except i is conceptual... Btw i is a representation for negatives under the radical which don't exist.
November 12th, 2006
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The square root of any negative number (-x) equals the square root of that number's opposite (x) times the imaginary unit (i). The imaginary unit squared (i^2) equals negative one (-1).
November 12th, 2006
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this magic of math is explained in a junior high algebra class
November 12th, 2006
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tru, except if you square root both sides, you need to add a "plus or minus" to the constant.
November 12th, 2006
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The "plus or minus" is omitted because only the positive square root is considered when calculating with the imaginary unit.
November 12th, 2006
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yeah.. everyone understands this.
November 12th, 2006
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Obviously there's a logical fallacy here, which proves that you suck, not maths. In this case, it's the fact that when you root a square, it's plus/minus, not just the positive root, like you took (the root of 1 being both minus one and plus one). Clearly, by the definition of the imaginary unit, the positive root is nonsensical and can be disregarded.
November 12th, 2006
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MATH
November 12th, 2006
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ZOMG MATH HACKS!
November 12th, 2006
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What's being proven is that |-1| = |1|. He left off the absolute value bars to look cool, but is blatantly wrong.
November 12th, 2006
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Add the "WTF BOOOOOOOM!!!!!!!!" once it shows -1=1
November 12th, 2006
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Actually, the logical fallacy has nothing to do with the plus/minus sign. If you want to know where the fallacy is, it lies in that when you multiply two square roots, you get the square root of the two variables under the radical sign [e.g. the square root of (a) times the square root of (b) equals the square root of (ab)] This law only applies to positive real numbers, wherein lies the fallacy.
November 12th, 2006
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Nope, nothing to do with absolute values. Nice try, though.
November 12th, 2006
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Sorry, didn't look through it carefully (it goes by quickly so I took it apart in ImageReady) and now I see it :D Extra star because yer crafty.
November 12th, 2006
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But it is an imaginary unit... so the whole equation would be impossible, seeing as any REAL number times itself is positive. Take algebra again.
November 12th, 2006
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I'm pretty sure I know it's impossible....but still interesting. Considering that I explained exactly why the statement is impossible above, which has nothing to do with your reasoning, I suggest that YOU take algebra again, and maybe you will realize that equations with imaginary units are infact possible.