e+π=6 which is rational
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How to spot an engineer
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Claim: Either e+π or eπ is irrational. Proof. Since both e and π are transcendental numbers (i.e. not roots of a polynomial with rational coefficients), the polynomial p(x) = (x-e)(x-π) = x²-(e+π)x+eπ must have at least one irrational coefficient, either e+π or eπ. ■
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I don't understand the either or part. Why can't they both be irrational?
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@__anthonyng @makagutu_o -
What about √-1
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It can further be shown that if e + π proves to be rational, e - π must be irrational, and vice versa.
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Exclusively or?
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But not both ?
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Both of course are transcential. Has anybody proven that there are an infinite number of them?
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