And sqrt(2)^sqrt(2) is irrational by the way: https://en.wikipedia.org/wiki/Gelfond%E2%80%93Schneider_theorem …
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In the "If not," case, you haven't shown that x is an irrational number :)
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i can always count on you, Keshav.
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I want to marry this proof
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There's a Mister Brouwer here, he'd like to have a little word with you about your so-called "proof"...
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Irrational but still algebraic (which form a countable set).
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How do I know I've been coding in C-style languages too much? For a moment I thought we were talking about the bit-wise XOR of x and y.
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A shorter proof: e^(ln 2) = 2.
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<the ghost of heyting weeps gently on my shoulder>
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Exactly - this is the classic example of a non-constructive proof.
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