若多项式函数列[tex=3.429x1.357]rs1NJeb245xTnFm4wHvOkDLjwQTKVfHV8LjLj/z71ck=[/tex] 在 [tex=4.786x1.357]WafKDm5071vVz9IYJgBhj8LbdrnQF2M50OcMtr5E7Yg=[/tex]上一致收敛于函数f(x)，则f(x)必是多项式函数。

设[tex=3.429x1.357]Z36AEPLbx4JfyrHPfLY1gg==[/tex]具有性质F，[tex=3.571x1.357]+06OwmLRwFoUAk4Z/SZg7Q==[/tex]具有性质G，命题“对所有x而言，若x有性质F，则x就有性质G”的符号化形式为

查表求[tex=3.429x1.357]9Gcht79O0y4LbGut7USjvA==[/tex] 。

证明[tex=1.857x1.357]BGkv0wKMIn2R4tUsMDFEFA==[/tex]是[tex=3.429x1.357]pweQz6vYdJSfN1APBJuJ8Q==[/tex]的当且仅当[tex=1.857x1.357]BGkv0wKMIn2R4tUsMDFEFA==[/tex]是[tex=3.429x1.357]pweQz6vYdJSfN1APBJuJ8Q==[/tex]的且[tex=1.857x1.357]QPi3lZKJ+q/B5QY5cuDuQg==[/tex]是[tex=3.429x1.357]Ax9d9CRxEVwtmbP/JF3yLQ==[/tex]的。

代数系统 [tex=3.429x1.357]dOdS9oTt8d627KTDGvWWtw==[/tex]定义如下：[tex=8.0x6.071]I08GkjPu5ilZ1cL3oVOjRDthbI6b9yBAb3FYfmWx9FVB2hL1r5K1ov8ijWjb4j3dIc5gclQL4uHwsbZdiP02cBveSlxsmIsQEmtdfuWbPigpHPNXKUuvY6lyC6Piq8SmgVIkDNsDqbVaaCaMce3tp9NhuC+wQ/Q4wa+pRbvn6bwWUziJyPli6hPB55gidqCb0lr7J1dhWHNxrEPtpWoGnh41n2MRY9ImuLCVL0Ca3WgglLL0NzUncKkDfT9pFZ1dQ2BCNaLrgNDzcn1suMaHOA==[/tex][tex=7.714x5.643]I08GkjPu5ilZ1cL3oVOjROvAfeDUalB11ixL4Nf3qb6/dwfQo6AWHDXxVrsHxBo4u2kvMAcbGmcHnCWRp97rBM3fVpJaYdUinjRA7CklEicRx8NZMR6ym5WO465IKBrv9syouyl1sPXBtlw58ZvHsfsOWhaEa0doiKT+EkNM8uIZjv5H8clIQyB7JZHOlrgBsLCVE4j2ABQ81T/FJWG3RAzofMO5NLzoYhvmOegDoOWeGHICMVXwLJqiyLYFPRxVGndWYrt62X5ygIMW0SiUFA==[/tex]证明：[tex=3.429x1.357]dOdS9oTt8d627KTDGvWWtw==[/tex]是一个域

代数系统 [tex=3.429x1.357]dOdS9oTt8d627KTDGvWWtw==[/tex]定义如下：[tex=8.0x6.071]I08GkjPu5ilZ1cL3oVOjRDthbI6b9yBAb3FYfmWx9FVB2hL1r5K1ov8ijWjb4j3dIc5gclQL4uHwsbZdiP02cBveSlxsmIsQEmtdfuWbPigpHPNXKUuvY6lyC6Piq8SmgVIkDNsDqbVaaCaMce3tp9NhuC+wQ/Q4wa+pRbvn6bwWUziJyPli6hPB55gidqCb0lr7J1dhWHNxrEPtpWoGnh41n2MRY9ImuLCVL0Ca3WgglLL0NzUncKkDfT9pFZ1dQ2BCNaLrgNDzcn1suMaHOA==[/tex][tex=7.714x5.643]I08GkjPu5ilZ1cL3oVOjROvAfeDUalB11ixL4Nf3qb6/dwfQo6AWHDXxVrsHxBo4u2kvMAcbGmcHnCWRp97rBM3fVpJaYdUinjRA7CklEicRx8NZMR6ym5WO465IKBrv9syouyl1sPXBtlw58ZvHsfsOWhaEa0doiKT+EkNM8uIZjv5H8clIQyB7JZHOlrgBsLCVE4j2ABQ81T/FJWG3RAzofMO5NLzoYhvmOegDoOWeGHICMVXwLJqiyLYFPRxVGndWYrt62X5ygIMW0SiUFA==[/tex]证明：[tex=3.429x1.357]dOdS9oTt8d627KTDGvWWtw==[/tex]是一个域

代数系统 [tex=3.429x1.357]dOdS9oTt8d627KTDGvWWtw==[/tex]定义如下：[tex=8.0x6.071]I08GkjPu5ilZ1cL3oVOjRDthbI6b9yBAb3FYfmWx9FVB2hL1r5K1ov8ijWjb4j3dIc5gclQL4uHwsbZdiP02cBveSlxsmIsQEmtdfuWbPigpHPNXKUuvY6lyC6Piq8SmgVIkDNsDqbVaaCaMce3tp9NhuC+wQ/Q4wa+pRbvn6bwWUziJyPli6hPB55gidqCb0lr7J1dhWHNxrEPtpWoGnh41n2MRY9ImuLCVL0Ca3WgglLL0NzUncKkDfT9pFZ1dQ2BCNaLrgNDzcn1suMaHOA==[/tex][tex=7.714x5.643]I08GkjPu5ilZ1cL3oVOjROvAfeDUalB11ixL4Nf3qb6/dwfQo6AWHDXxVrsHxBo4u2kvMAcbGmcHnCWRp97rBM3fVpJaYdUinjRA7CklEicRx8NZMR6ym5WO465IKBrv9syouyl1sPXBtlw58ZvHsfsOWhaEa0doiKT+EkNM8uIZjv5H8clIQyB7JZHOlrgBsLCVE4j2ABQ81T/FJWG3RAzofMO5NLzoYhvmOegDoOWeGHICMVXwLJqiyLYFPRxVGndWYrt62X5ygIMW0SiUFA==[/tex]证明：[tex=3.429x1.357]dOdS9oTt8d627KTDGvWWtw==[/tex]是一个域

代数系统 [tex=3.429x1.357]dOdS9oTt8d627KTDGvWWtw==[/tex]定义如下：[tex=8.0x6.071]I08GkjPu5ilZ1cL3oVOjRDthbI6b9yBAb3FYfmWx9FVB2hL1r5K1ov8ijWjb4j3dIc5gclQL4uHwsbZdiP02cBveSlxsmIsQEmtdfuWbPigpHPNXKUuvY6lyC6Piq8SmgVIkDNsDqbVaaCaMce3tp9NhuC+wQ/Q4wa+pRbvn6bwWUziJyPli6hPB55gidqCb0lr7J1dhWHNxrEPtpWoGnh41n2MRY9ImuLCVL0Ca3WgglLL0NzUncKkDfT9pFZ1dQ2BCNaLrgNDzcn1suMaHOA==[/tex][tex=7.714x5.643]I08GkjPu5ilZ1cL3oVOjROvAfeDUalB11ixL4Nf3qb6/dwfQo6AWHDXxVrsHxBo4u2kvMAcbGmcHnCWRp97rBM3fVpJaYdUinjRA7CklEicRx8NZMR6ym5WO465IKBrv9syouyl1sPXBtlw58ZvHsfsOWhaEa0doiKT+EkNM8uIZjv5H8clIQyB7JZHOlrgBsLCVE4j2ABQ81T/FJWG3RAzofMO5NLzoYhvmOegDoOWeGHICMVXwLJqiyLYFPRxVGndWYrt62X5ygIMW0SiUFA==[/tex]证明：[tex=3.429x1.357]dOdS9oTt8d627KTDGvWWtw==[/tex]是一个域

代数系统 [tex=3.429x1.357]dOdS9oTt8d627KTDGvWWtw==[/tex]定义如下：[tex=8.0x6.071]I08GkjPu5ilZ1cL3oVOjRDthbI6b9yBAb3FYfmWx9FVB2hL1r5K1ov8ijWjb4j3dIc5gclQL4uHwsbZdiP02cBveSlxsmIsQEmtdfuWbPigpHPNXKUuvY6lyC6Piq8SmgVIkDNsDqbVaaCaMce3tp9NhuC+wQ/Q4wa+pRbvn6bwWUziJyPli6hPB55gidqCb0lr7J1dhWHNxrEPtpWoGnh41n2MRY9ImuLCVL0Ca3WgglLL0NzUncKkDfT9pFZ1dQ2BCNaLrgNDzcn1suMaHOA==[/tex][tex=7.714x5.643]I08GkjPu5ilZ1cL3oVOjROvAfeDUalB11ixL4Nf3qb6/dwfQo6AWHDXxVrsHxBo4u2kvMAcbGmcHnCWRp97rBM3fVpJaYdUinjRA7CklEicRx8NZMR6ym5WO465IKBrv9syouyl1sPXBtlw58ZvHsfsOWhaEa0doiKT+EkNM8uIZjv5H8clIQyB7JZHOlrgBsLCVE4j2ABQ81T/FJWG3RAzofMO5NLzoYhvmOegDoOWeGHICMVXwLJqiyLYFPRxVGndWYrt62X5ygIMW0SiUFA==[/tex]证明：[tex=3.429x1.357]dOdS9oTt8d627KTDGvWWtw==[/tex]是一个域

代数系统 [tex=3.429x1.357]dOdS9oTt8d627KTDGvWWtw==[/tex]定义如下：[tex=8.0x6.071]I08GkjPu5ilZ1cL3oVOjRDthbI6b9yBAb3FYfmWx9FVB2hL1r5K1ov8ijWjb4j3dIc5gclQL4uHwsbZdiP02cBveSlxsmIsQEmtdfuWbPigpHPNXKUuvY6lyC6Piq8SmgVIkDNsDqbVaaCaMce3tp9NhuC+wQ/Q4wa+pRbvn6bwWUziJyPli6hPB55gidqCb0lr7J1dhWHNxrEPtpWoGnh41n2MRY9ImuLCVL0Ca3WgglLL0NzUncKkDfT9pFZ1dQ2BCNaLrgNDzcn1suMaHOA==[/tex][tex=7.714x5.643]I08GkjPu5ilZ1cL3oVOjROvAfeDUalB11ixL4Nf3qb6/dwfQo6AWHDXxVrsHxBo4u2kvMAcbGmcHnCWRp97rBM3fVpJaYdUinjRA7CklEicRx8NZMR6ym5WO465IKBrv9syouyl1sPXBtlw58ZvHsfsOWhaEa0doiKT+EkNM8uIZjv5H8clIQyB7JZHOlrgBsLCVE4j2ABQ81T/FJWG3RAzofMO5NLzoYhvmOegDoOWeGHICMVXwLJqiyLYFPRxVGndWYrt62X5ygIMW0SiUFA==[/tex]证明：[tex=3.429x1.357]dOdS9oTt8d627KTDGvWWtw==[/tex]是一个域