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Originally Posted by daking
Imaginary numbers "exist" to the same extent that Real numbers "exist". Further more there is no orderedness in complex (imaginary) numbers compared to purely real numbers, so you cant really say they are "bigger" without using a different metric |a+bi| .
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Yeah, that was supposed to be a humorous remark. I should've known that a math joke was doomed to fail. I know that imaginary numbers do exist, they were only termed imaginary because the first people to work with them weren't really comfortable (square root of a negative number? WTF!). I hadn't really thought about the fact that you can't compare imaginary and real numbers. I suppose the opposite names should have clued me in.
On another note, my teacher got fed up with the proof, and crossed it out on the grounds that you can't define x twice.
