-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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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.
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.
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.
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