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2007-11-13
<p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span style="; FONT-FAMILY: 宋体; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">“如果</span><span lang="EN-US" style=";"><font face="Times New Roman">y</font></span><span style="; FONT-FAMILY: 宋体; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">大于等于</span><span lang="EN-US" style=";"><font face="Times New Roman">x</font></span><span style="; FONT-FAMILY: 宋体; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">,且</span><span lang="EN-US" style=";"><font face="Times New Roman">y</font></span><span style="; FONT-FAMILY: 宋体; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">不等于</span><span lang="EN-US" style=";"><font face="Times New Roman">x.</font></span><span style="; FONT-FAMILY: 宋体; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">意味着</span><span lang="EN-US" style=";"><font face="Times New Roman">y</font></span><span style="; FONT-FAMILY: 宋体; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">优于</span><span lang="EN-US" style=";"><font face="Times New Roman">x</font></span><span style="; FONT-FAMILY: 宋体; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">,就说偏好关系是严格单调的。”</span><span lang="EN-US" style=";"><p></p></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span lang="EN-US" style=";"><font face="Times New Roman"><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span></font></span><span style="; FONT-FAMILY: 宋体; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">在这里,</span><span lang="EN-US" style=";"><font face="Times New Roman">y </font></span><span style="; FONT-FAMILY: 宋体; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">大于等于</span><span lang="EN-US" style=";"><font face="Times New Roman">x</font></span><span style="; FONT-FAMILY: 宋体; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">,是不是说前者至少有一个元素大于后者,而其他的元素不比后者的小?如果是的话,那么是不是意味着</span><span lang="EN-US" style=";"><font face="Times New Roman">y</font></span><span style="; FONT-FAMILY: 宋体; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">不等于</span><span lang="EN-US" style=";"><font face="Times New Roman">x</font></span><span style="; FONT-FAMILY: 宋体; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">?如果前面的成立,就说明</span><span lang="EN-US" style=";"><font face="Times New Roman">y</font></span><span style="; FONT-FAMILY: 宋体; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">大于等于</span><span lang="EN-US" style=";"><font face="Times New Roman">x</font></span><span style="; FONT-FAMILY: 宋体; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">已经包含了</span><span lang="EN-US" style=";"><font face="Times New Roman">y</font></span><span style="; FONT-FAMILY: 宋体; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">不等于</span><span lang="EN-US" style=";"><font face="Times New Roman">x</font></span><span style="; FONT-FAMILY: 宋体; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">。那么定义的后面怎么又要加上</span><span lang="EN-US" style=";"><font face="Times New Roman">y</font></span><span style="; FONT-FAMILY: 宋体; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">不等于</span><span lang="EN-US" style=";"><font face="Times New Roman">x</font></span><span style="; FONT-FAMILY: 宋体; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman";">?如何理解偏好关系是严格单调这个定义?</span><span lang="EN-US" style=";"><p></p></span></p>
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2007-11-13 21:25:00

向量非负,等价于,该向量中每个分量都非负。

向量a不小于向量b,等价于,a-b非负。

向量a不等于向量b,等价于,a-b中至少有一个分量非零。

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2007-11-13 23:28:00
Y大于等于X应该是说,Y里的元素都是大于等于X里的对应元素,可能有些大于,有些是等于,或者都是等于,都是大于.所以加上Y不等于X的条件就说明不是第三种情况.
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2007-11-14 08:59:00
帮楼主大大顶了啊
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2007-11-14 17:18:00
“y 大于等于x,y不等于x”的数学符号表示是>=(等号在大于号的下面)意思是说对任意的i,yi大于等于xi,但至少存在j使得yj严格大于xj。而“y 大于等于x”的数学符号表示是>_ (横线在大于号下面),然后对于前面的情况,如果我们说“y优于x”,那么我们称偏好关系严格单调。
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