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The mean-value theorem (of differential calculus) can be used to prove that Liouville numbers are transcendental. The proof is quite simple, taking only a couple of lines. See Theorem 191 of Hardy and Wright's "An Introduction to the Theory of Numbers" on Google books. I believe, historically, that these were the first known examples of transcendental numbers. |
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The mean-value theorem (of differential calculus) can be used to prove that Liouville numbers are transcendental. I believe, historically, that these were the first known examples of transcendental numbers. |
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