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A Little Challenge Problem for Real Number Theorem ... - Lemma 1!

A Little Challenge Problem for Real Number Theorem ... - Lemma 1!

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A Little Challenge Problem for Real Number Theorem Proving 4 ✬ Encoding sin in a bounded concave γ. II ✩ Answer: yes! Here are γ, γ ′ and γ ′′ for K = M = 1: 2 1 gamma0(x) Dgamma(x) DDgamma(x) 0 −1 −2 −3 −4 −5 −6 −7 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 ✫ Can you prove γ ′′ < 0? ✪

A Little Challenge Problem for Real Number Theorem Proving 5 ✬ Encoding sin in a bounded concave γ. III ✩ Answer: ah! well, I can prove it for K = 2 and M ≥ 9: 3 2 gamma0(x) Dgamma(x) DDgamma(x) 1 0 −1 −2 −3 −4 −5 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 ✫ Challenge: is there any automation to help out there? ✪

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