{"id":58466,"date":"2025-08-16T11:04:53","date_gmt":"2025-08-16T03:04:53","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/58466.html"},"modified":"2025-08-16T11:04:53","modified_gmt":"2025-08-16T03:04:53","slug":"%e5%af%bb%e6%89%be%e5%ae%a2%e6%88%b7%e5%88%86%e7%b1%bb%e7%9a%84%e5%85%85%e8%a6%81%e6%9d%a1%e4%bb%b6","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/58466.html","title":{"rendered":"\u5bfb\u627e\u5ba2\u6237\u5206\u7c7b\u7684\u5145\u8981\u6761\u4ef6"},"content":{"rendered":"<h4>\u5ba2\u6237\u5206\u7c7b\u7684\u5145\u8981\u6761\u4ef6<\/h4>\n<p>\u5ba2\u6237\u5206\u7c7b\u662f\u6307\u6839\u636e\u5ba2\u6237\u7684\u5c5e\u6027\uff08\u5982\u5e74\u9f84\u3001\u6536\u5165\u3001\u8d2d\u4e70\u884c\u4e3a\u7b49\uff09\u5c06\u5ba2\u6237\u5212\u5206\u4e3a\u4e0d\u540c\u7c7b\u522b\u7684\u8fc7\u7a0b\u3002\u5145\u8981\u6761\u4ef6\uff08\u5373\u5fc5\u8981\u4e14\u5145\u5206\u6761\u4ef6\uff09\u610f\u5473\u7740\u4e00\u4e2a\u6761\u4ef6\u5fc5\u987b\u6210\u7acb\uff08\u5fc5\u8981\uff09\uff0c\u4e14\u53ea\u8981\u8be5\u6761\u4ef6\u6210\u7acb\uff0c\u5206\u7c7b\u5c31\u80fd\u51c6\u786e\u5b8c\u6210\uff08\u5145\u5206\uff09\u3002\u5728\u6570\u5b66\u4e0a\uff0c\u8fd9\u901a\u5e38\u6d89\u53ca\u5206\u7c7b\u51fd\u6570\u6216\u51b3\u7b56\u89c4\u5219\u7684\u5b8c\u7f8e\u6027\u3002\u4e0b\u9762\u6211\u5c06\u9010\u6b65\u89e3\u91ca\u5e76\u63a8\u5bfc\u5ba2\u6237\u5206\u7c7b\u7684\u5145\u8981\u6761\u4ef6\u3002<\/p>\n<h5>\u6b65\u9aa41: \u7406\u89e3\u5ba2\u6237\u5206\u7c7b\u95ee\u9898<\/h5>\n<ul>\n<li>\u5047\u8bbe\u6709\u4e00\u4e2a\u5ba2\u6237\u96c6\u5408<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">CC<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><\/span><\/span><\/span><\/span>\uff0c\u6bcf\u4e2a\u5ba2\u6237<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">c\u2208Cc \\\\in C<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5782em;vertical-align: -0.0391em\"><\/span><span class=\"mord mathnormal\">c<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2208<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><\/span><\/span><\/span><\/span>\u6709\u4e00\u7ec4\u5c5e\u6027\u5411\u91cf<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">xx<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span>\uff08\u4f8b\u5982<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">x=(\u5e74\u9f84,\u6536\u5165,\u2026\u2009)x = (\u5e74\u9f84, \u6536\u5165, \\\\dots)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord cjk_fallback\">\u5e74\u9f84<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord cjk_fallback\">\u6536\u5165<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\">\u2026<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\uff09\u3002<\/li>\n<li>\u76ee\u6807\u662f\u5c06<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">CC<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><\/span><\/span><\/span><\/span>\u5212\u5206\u4e3a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">kk<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><\/span>\u4e2a\u4e92\u65a5\u7684\u7c7b\u522b<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">Y={<br \/>\n     y1,y2,\u2026,yk}Y = \\\\{y_1, y_2, \\\\dots, y_k\\\\}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.2222em\">Y<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">{<br \/>\n       <\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\">\u2026<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">}<\/span><\/span><\/span><\/span><\/span>\uff0c\u5176\u4e2d<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">yiy_i<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4ee3\u8868\u4e00\u4e2a\u7c7b\u522b\uff08\u5982\u201c\u9ad8\u4ef7\u503c\u5ba2\u6237\u201d\u6216\u201c\u4f4e\u4ef7\u503c\u5ba2\u6237\u201d\uff09\u3002<\/li>\n<li>\u5206\u7c7b\u8fc7\u7a0b\u7531\u4e00\u4e2a\u5206\u7c7b\u51fd\u6570<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">f:X\u2192Yf: X \\\\to Y<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">:<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0785em\">X<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2192<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.2222em\">Y<\/span><\/span><\/span><\/span><\/span>\u5b9a\u4e49\uff0c\u5176\u4e2d<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">XX<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0785em\">X<\/span><\/span><\/span><\/span><\/span>\u662f\u5c5e\u6027\u7a7a\u95f4\uff0c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">f(x)f(x)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u8f93\u51fa\u5ba2\u6237<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">xx<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span>\u7684\u7c7b\u522b\u3002<\/li>\n<\/ul>\n<h5>\u6b65\u9aa42: \u5b9a\u4e49\u5145\u8981\u6761\u4ef6<\/h5>\n<p>\u5145\u8981\u6761\u4ef6\u5173\u6ce8\u5206\u7c7b\u7684\u51c6\u786e\u6027\uff1a\u5206\u7c7b\u662f\u5b8c\u7f8e\u7684\u5f53\u4e14\u4ec5\u5f53\u6bcf\u4e2a\u5ba2\u6237\u90fd\u88ab\u6b63\u786e\u5206\u914d\u5230\u5176\u771f\u5b9e\u7c7b\u522b\u3002\u6570\u5b66\u4e0a\uff0c\u8fd9\u53ef\u4ee5\u8868\u8ff0\u4e3a\uff1a<\/p>\n<ul>\n<li>\u5fc5\u8981\u6761\u4ef6\uff1a\u5982\u679c\u5206\u7c7b\u6b63\u786e\uff0c\u5219\u5c5e\u6027<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">xx<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span>\u5fc5\u987b\u80fd\u552f\u4e00\u786e\u5b9a\u7c7b\u522b<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">yy<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><\/span><\/span><\/span><\/span>\uff08\u5373\u6ca1\u6709\u6b67\u4e49\uff09\u3002<\/li>\n<li>\u5145\u5206\u6761\u4ef6\uff1a\u5982\u679c\u5c5e\u6027<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">xx<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span>\u80fd\u552f\u4e00\u786e\u5b9a\u7c7b\u522b<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">yy<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><\/span><\/span><\/span><\/span>\uff0c\u5219\u5206\u7c7b\u4e00\u5b9a\u6b63\u786e\u3002<\/li>\n<li>\u5145\u8981\u6761\u4ef6\uff1a\u5206\u7c7b\u51fd\u6570<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">ff<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><\/span><\/span><\/span><\/span>\u6ee1\u8db3\u5bf9\u6240\u6709<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">x\u2208Xx \\\\in X<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5782em;vertical-align: -0.0391em\"><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right: 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