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Re: .999~ = 1
How about this proof:
given: e^(i * pi) = -1
e^(3 * i * pi) = e^(i * pi) * e^(i * pi) * e^(i * pi) = -1 * -1 * -1 = -1
therefore:
e^(i * pi) = e^(3 * i * pi)
ln e^(i * pi) = ln e^(3 * i * pi)
(i * pi) ln e = (3 * i * pi) ln e
i * pi = 3 * i * pi
1 = 3
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