FindInstance为{}不能证明无解

hbghlyj

用.7能找到满足不等式的$x$,而7/10不能找到:

1. ϵ=.7;FindInstance[{Cos[x]-ϵ/2 x Sin[x]-Cos[x Sqrt[1+ϵ]]>0,0<x<ϵ},x]

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{{x -> 6.55933*10^-9}}

1. ϵ=7/10;FindInstance[{Cos[x]-ϵ/2 x Sin[x]-Cos[x Sqrt[1+ϵ]]>0,0<x<ϵ},x]

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FindInstance::nint: Warning: FindInstance used numeric integration to show that the solution set found is complete.
{}
用.1能找到满足不等式的$x$,而1/10不能找到:

1. ϵ=.1;FindInstance[{Cos[x]-ϵ/2 x Sin[x]-Cos[x Sqrt[1+ϵ]]>0,0<x<ϵ},x]

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{{x -> 8.83286*10^-8}}

1. ϵ=1/10;FindInstance[{Cos[x]-ϵ/2 x Sin[x]-Cos[x Sqrt[1+ϵ]]>0,0<x<ϵ},x]

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{}

hbghlyj

像MathematicaSE所写的

If FindInstance[expr, vars, dom] returns no instances - {}, it does not mean (in general) there are no solutions, i.e. it does not prove anything here.