<p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 21pt; mso-char-indent-count: 2.0;"><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">下面的资料引自华罗庚在</span><span lang="EN-US"><font face="Times New Roman">79</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">年左右写的一本书:</span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 21pt; mso-char-indent-count: 2.0;"><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';"></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 21pt; mso-char-indent-count: 2.0;"><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';"> 在<font color="#f70909">自然数</font>中,我们将那些可以被</span><span lang="EN-US"><font face="Times New Roman">2</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">整除的数叫作<font color="#ff0000">偶数</font>,如</span></p><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';"> </span><span lang="EN-US"><font face="Times New Roman">2</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">、</span><span lang="EN-US"><font face="Times New Roman">4</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">、</span><span lang="EN-US"><font face="Times New Roman">6</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">、</span><span lang="EN-US"><font face="Times New Roman">8</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">、</span><span lang="EN-US"><font face="Times New Roman">10</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">、</span><span lang="EN-US"><font face="Times New Roman">...等</font></span></p><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';"> 剩下的那些自然数就叫作<font color="#f70909">奇数</font>,如</span></p><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';"> </span><span lang="EN-US"><font face="Times New Roman">1</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">、</span><span lang="EN-US"><font face="Times New Roman">3</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">、</span><span lang="EN-US"><font face="Times New Roman">5</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">、</span><span lang="EN-US"><font face="Times New Roman">7</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">、</span><span lang="EN-US"><font face="Times New Roman">9</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">、</span><span lang="EN-US"><font face="Times New Roman">...等</font></span></p><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';"> 这样,所有的自然数就被分成了偶数和奇数两大类。另一方面,除去</span><span lang="EN-US"><font face="Times New Roman">1</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">以外,有的数除了</span><span lang="EN-US"><font face="Times New Roman">1</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">和它本身以外,不能再被别的整数整除,如</span></p><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';"> </span><span lang="EN-US"><font face="Times New Roman">2</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">、</span><span lang="EN-US"><font face="Times New Roman">3</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">、</span><span lang="EN-US"><font face="Times New Roman">5</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">、</span><span lang="EN-US"><font face="Times New Roman">7</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">、</span><span lang="EN-US"><font face="Times New Roman">11</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">、</span><span lang="EN-US"><font face="Times New Roman">13</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">、</span><span lang="EN-US"><font face="Times New Roman">17</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">、</span><span lang="EN-US"><font face="Times New Roman">...</font></span></p><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';">等,这种数称作<font color="#ff3300">素数</font></span><font color="#ff3300"><span lang="EN-US"><font face="Times New Roman">(</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">也称质数</span><span lang="EN-US"><font face="Times New Roman">)</font></span></font><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">。</span></p><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';">有的数除了</span><span lang="EN-US"><font face="Times New Roman">1</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">和它本身以外,还能被别的整数整除,这种数就叫<font color="#f70909">合数</font>,如</span></p><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';"> </span><span lang="EN-US"><font face="Times New Roman">4</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">、</span><span lang="EN-US"><font face="Times New Roman">6</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">、</span><span lang="EN-US"><font face="Times New Roman">8</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">、</span><span lang="EN-US"><font face="Times New Roman">9</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">、</span><span lang="EN-US"><font face="Times New Roman">10</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">、</span><span lang="EN-US"><font face="Times New Roman">12</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">、</span><span lang="EN-US"><font face="Times New Roman">14</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">、</span><span lang="EN-US"><font face="Times New Roman">...</font></span></p><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';">等,就是合数。</span></p><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';"></span><span lang="EN-US"><font face="Times New Roman">1</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">这个数比较特殊,它既不算素数也不算合数。</span></p><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';">这样,所有的<font color="#ff0000">自然数就又被分为</font></span><span lang="EN-US"><font face="Times New Roman" color="#ff0000">1</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';"><font color="#ff0000">和素数、合数三类</font>。自然数的这种分类法,要比它分为奇数和偶数两大类要复杂多了。</span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 21.75pt;"><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">由此可见,偶数以及素数、合数的概念应该都是排除了</span><span lang="EN-US"><font face="Times New Roman">0</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">所下的定义。因此,现在我们再考虑这些概念的时候也应该把</span><span lang="EN-US"><font face="Times New Roman">0</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">排除在外。</span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">这些概念的定义是不包括</span><span lang="EN-US"><font face="Times New Roman">0</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">的。所以所有的自然数都是指不包括<span lang="EN-US"><font face="Times New Roman">0</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">的。</span></span></p>
[此贴子已经被作者于2007-6-13 22:45:49编辑过]
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