I wanna see the proof of Hillbert's 7th problem since this proof relies so heavily on it.
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Ikr, almost makes the proof feel incomplete
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You could use a "weaker" theorem that came first. Namely, that if a is algebraic, e^a is transcendental. The theorem goes back to 1882 when Lindemann proved it.
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But pi isn't algebraic
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Why is -i irrational?
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Not sure I understand why e^(i*pi) = -1 ...
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e^(i*pi) = -1 is Euler’s identity. Which is a special case of Euler’s formula: For any real number, x, e^(ix) = cos(x) + i*sin(x)
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Also I don't know why u assumed -i to be irrational. Irrational numbers are real numbers which are not rational. And -i clearly isn't real.
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Maybe because i is not rational, so "irrational" sounded good :) Sed tertium datur.
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