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[不等式] 4个不等式等价于3个不等式

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hbghlyj posted 2023-7-14 16:06 |Read mode
Last edited by hbghlyj 2023-7-14 16:12函数$f_1,f_2,f_3,f_4:\Bbb R^3\to\Bbb R$.
集合$A=\set{(x,y,z)\inR^3|f_1(x,y,z)\ge0,f_2(x,y,z)\ge0,f_3(x,y,z)\ge0,f_4(x,y,z)\ge0}$.
则存在函数$g,g_1,g_2,g_3:\Bbb R^3\to\Bbb R$使
$A=\set{g(x,y,z)|(x,y,z)\inR^3,g_1(x,y,z)\ge0,g_2(x,y,z)\ge0,g_3(x,y,z)\ge0}$?


这个对么
如果不对,把$f_1,f_2,f_3,f_4$限定为多项式,这个对吗?
如果还不对,把$f_1,f_2,f_3,f_4$限定为一次多项式,这个对吗?

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