http://wiki.googology.top/index.php?action=history&feed=atom&title=Dropping 2026-04-22T15:25:33Z 本wiki上该页面的版本历史 MediaWiki 1.43.1 http://wiki.googology.top/index.php?title=Dropping&diff=2910&oldid=prev 2026-03-01T07:35:44Z

<p><span class="autocomment">M 记号</span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="zh-Hans-CN"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">←上一版本</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">2026年3月1日 (日) 15:35的版本</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l4">第4行：</td> <td colspan="2" class="diff-lineno">第4行：</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>M 记号实际上使用的是 2-dropping hydra 模式，而一般的 hydra 实际上是 1-dropping hydra。</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>M 记号实际上使用的是 2-dropping hydra 模式，而一般的 hydra 实际上是 1-dropping hydra。</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>比如 <del style="font-weight: bold; text-decoration: none;">p0</del>(<del style="font-weight: bold; text-decoration: none;">p1</del>+<del style="font-weight: bold; text-decoration: none;">p1</del>)，p1 向外找到 p0，然后进行迭代，得到 <del style="font-weight: bold; text-decoration: none;">p0</del>(<del style="font-weight: bold; text-decoration: none;">p1</del>+<del style="font-weight: bold; text-decoration: none;">p0</del>(<del style="font-weight: bold; text-decoration: none;">p1</del>+<del style="font-weight: bold; text-decoration: none;">p0</del>(<del style="font-weight: bold; text-decoration: none;">p1</del>+<del style="font-weight: bold; text-decoration: none;">..</del>))</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>比如 <ins style="font-weight: bold; text-decoration: none;">&lt;math&gt;p_0</ins>(<ins style="font-weight: bold; text-decoration: none;">p_1</ins>+<ins style="font-weight: bold; text-decoration: none;">p_1</ins>)<ins style="font-weight: bold; text-decoration: none;">&lt;/math&gt;</ins>，p1 向外找到 p0，然后进行迭代，得到 <ins style="font-weight: bold; text-decoration: none;">&lt;math&gt;p_0</ins>(<ins style="font-weight: bold; text-decoration: none;">p_1</ins>+<ins style="font-weight: bold; text-decoration: none;">p_0</ins>(<ins style="font-weight: bold; text-decoration: none;">p_1</ins>+<ins style="font-weight: bold; text-decoration: none;">p_0</ins>(<ins style="font-weight: bold; text-decoration: none;">p_1</ins>+<ins style="font-weight: bold; text-decoration: none;">\dots</ins>))<ins style="font-weight: bold; text-decoration: none;">)&lt;/math&gt;</ins></div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>而在 M 记号中 <del style="font-weight: bold; text-decoration: none;">p0</del>(<del style="font-weight: bold; text-decoration: none;">p0</del>(<del style="font-weight: bold; text-decoration: none;">p1</del>)+<del style="font-weight: bold; text-decoration: none;">p0</del>(<del style="font-weight: bold; text-decoration: none;">p1</del>)，p1 <del style="font-weight: bold; text-decoration: none;">向往找到等级更低的 </del>p0，得到 <del style="font-weight: bold; text-decoration: none;">p0</del>(<del style="font-weight: bold; text-decoration: none;">p1</del>)<del style="font-weight: bold; text-decoration: none;">，将其作为迭代子，继续向外找，得到，p0</del>(<del style="font-weight: bold; text-decoration: none;">p0</del>(<del style="font-weight: bold; text-decoration: none;">p1</del>)+<del style="font-weight: bold; text-decoration: none;">...</del>)<del style="font-weight: bold; text-decoration: none;">，然后进行迭代得到p0</del>(<del style="font-weight: bold; text-decoration: none;">p0</del>(<del style="font-weight: bold; text-decoration: none;">p1</del>)+<del style="font-weight: bold; text-decoration: none;">p0</del>(<del style="font-weight: bold; text-decoration: none;">p0</del>(<del style="font-weight: bold; text-decoration: none;">p1</del>)+<del style="font-weight: bold; text-decoration: none;">p0</del>(<del style="font-weight: bold; text-decoration: none;">p0</del>(<del style="font-weight: bold; text-decoration: none;">p1</del>)+<del style="font-weight: bold; text-decoration: none;">...</del>))。p1 实际上是 p_1(0)，像 [[序数坍缩函数#BOCF 简介|BOCF]] 中 <del style="font-weight: bold; text-decoration: none;">ψ_1</del>(0)=<del style="font-weight: bold; text-decoration: none;">Ω </del>一样，可以有 p_1(0)=<del style="font-weight: bold; text-decoration: none;">M，进一步还有 </del>p_1(p_1(0)=M^2<del style="font-weight: bold; text-decoration: none;">,</del>p_1(p_1(p_1(0))=M^M 这样，就能得到一般使用的 M 记号了。</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>而在 M 记号中 <ins style="font-weight: bold; text-decoration: none;">&lt;math&gt;p_0</ins>(<ins style="font-weight: bold; text-decoration: none;">p_0</ins>(<ins style="font-weight: bold; text-decoration: none;">p_1</ins>)+<ins style="font-weight: bold; text-decoration: none;">p_0</ins>(<ins style="font-weight: bold; text-decoration: none;">p_1)</ins>)<ins style="font-weight: bold; text-decoration: none;">&lt;/math&gt;</ins>，p1 <ins style="font-weight: bold; text-decoration: none;">向外找到等级更低的 </ins>p0，得到 <ins style="font-weight: bold; text-decoration: none;">&lt;math&gt;p_0</ins>(<ins style="font-weight: bold; text-decoration: none;">p_1</ins>)<ins style="font-weight: bold; text-decoration: none;">&lt;/math&gt;，将其作为迭代子，继续向外找，得到 &lt;math&gt;p_0</ins>(<ins style="font-weight: bold; text-decoration: none;">p_0</ins>(<ins style="font-weight: bold; text-decoration: none;">p_1</ins>)+<ins style="font-weight: bold; text-decoration: none;">\dots</ins>)<ins style="font-weight: bold; text-decoration: none;">&lt;/math&gt;，然后进行迭代得到 &lt;math&gt;p_0</ins>(<ins style="font-weight: bold; text-decoration: none;">p_0</ins>(<ins style="font-weight: bold; text-decoration: none;">p_1</ins>)+<ins style="font-weight: bold; text-decoration: none;">p_0</ins>(<ins style="font-weight: bold; text-decoration: none;">p_0</ins>(<ins style="font-weight: bold; text-decoration: none;">p_1</ins>)+<ins style="font-weight: bold; text-decoration: none;">p_0</ins>(<ins style="font-weight: bold; text-decoration: none;">p_0</ins>(<ins style="font-weight: bold; text-decoration: none;">p_1</ins>)+<ins style="font-weight: bold; text-decoration: none;">\dots)</ins>))<ins style="font-weight: bold; text-decoration: none;">&lt;/math&gt;</ins>。p1 实际上是 <ins style="font-weight: bold; text-decoration: none;">&lt;math&gt;</ins>p_1(0)<ins style="font-weight: bold; text-decoration: none;">&lt;/math&gt;</ins>，像 [[序数坍缩函数#BOCF 简介|BOCF]] 中 <ins style="font-weight: bold; text-decoration: none;">&lt;math&gt;\psi_1</ins>(0)=<ins style="font-weight: bold; text-decoration: none;">\Omega&lt;/math&gt; </ins>一样，可以有 <ins style="font-weight: bold; text-decoration: none;">&lt;math&gt;</ins>p_1(0)=<ins style="font-weight: bold; text-decoration: none;">M&lt;/math&gt;，进一步还有 &lt;math&gt;</ins>p_1(p_1(0<ins style="font-weight: bold; text-decoration: none;">)</ins>)=M^2<ins style="font-weight: bold; text-decoration: none;">&lt;/math&gt;、&lt;math&gt;</ins>p_1(p_1(p_1(0<ins style="font-weight: bold; text-decoration: none;">)</ins>))=M^M<ins style="font-weight: bold; text-decoration: none;">&lt;/math&gt; </ins>这样，就能得到一般使用的 M 记号了。</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>以下省略 p：</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>以下省略 p：</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>0(0(1(1(1))+0(1(1(1))：首先是最右边的 p1 向外找到等级更低的 0(1(1(1))，继续向外找到等级更低的 0(0(1(1(1))+<del style="font-weight: bold; text-decoration: none;">...</del>))，而 0(1(1(1))&gt;0(1(1(0))&gt;0(0(1(1(1))+<del style="font-weight: bold; text-decoration: none;">....</del>)，于是进行补层，得到 0(1(1(0(1(1(1))+0(1(1(1))))<del style="font-weight: bold; text-decoration: none;">，进行迭代得到，0</del>(1(1(0(1(1(1))+0(1(1(0(1(1(1))+0(1(1(0(1(1(1))+<del style="font-weight: bold; text-decoration: none;">...</del>)))))))))，放回原来的层，得到 0(0(1(1(1))+0(1(1(0(1(1(1))+0(1(1(0(1(1(1)) +0(1(1(0(1(1(1))+<del style="font-weight: bold; text-decoration: none;">...</del>))))))))))</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;math&gt;</ins>0(0(1(1(1))+0(1(1(1))<ins style="font-weight: bold; text-decoration: none;">))&lt;/math&gt;</ins>：首先是最右边的 p1 向外找到等级更低的 <ins style="font-weight: bold; text-decoration: none;">&lt;math&gt;</ins>0(1(1(1))<ins style="font-weight: bold; text-decoration: none;">)&lt;/math&gt;</ins>，继续向外找到等级更低的 <ins style="font-weight: bold; text-decoration: none;">&lt;math&gt;</ins>0(0(1(1(1))+<ins style="font-weight: bold; text-decoration: none;">\dots</ins>))<ins style="font-weight: bold; text-decoration: none;">&lt;/math&gt;</ins>，而 <ins style="font-weight: bold; text-decoration: none;">&lt;math&gt;</ins>0(1(1(1<ins style="font-weight: bold; text-decoration: none;">)</ins>))&gt;0(1(1(0<ins style="font-weight: bold; text-decoration: none;">)</ins>))&gt;0(0(1(1(1))+<ins style="font-weight: bold; text-decoration: none;">\dots</ins>)<ins style="font-weight: bold; text-decoration: none;">)&lt;/math&gt;</ins>，于是进行补层，得到 <ins style="font-weight: bold; text-decoration: none;">&lt;math&gt;</ins>0(1(1(0(1(1(1))+0(1(1(1))))<ins style="font-weight: bold; text-decoration: none;">))&lt;/math&gt;，进行迭代得到 &lt;math&gt;0</ins>(1(1(0(1(1(1))+0(1(1(0(1(1(1))+0(1(1(0(1(1(1))+<ins style="font-weight: bold; text-decoration: none;">\dots</ins>)))))))))<ins style="font-weight: bold; text-decoration: none;">&lt;/math&gt;</ins>，放回原来的层，得到 <ins style="font-weight: bold; text-decoration: none;">&lt;math&gt;</ins>0(0(1(1(1))+0(1(1(0(1(1(1))+0(1(1(0(1(1(1)) +0(1(1(0(1(1(1))+<ins style="font-weight: bold; text-decoration: none;">\dots</ins>))))))))))<ins style="font-weight: bold; text-decoration: none;">&lt;/math&gt;</ins></div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>0(0(1(1(1)))+0(1(1(0(1(1(1)))))+1(1(0(1(1(1)))))))</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;math&gt;</ins>0(0(1(1(1)))+0(1(1(0(1(1(1)))))+1(1(0(1(1(1)))))))<ins style="font-weight: bold; text-decoration: none;">&lt;/math&gt;</ins></div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>p1 向外找到 0(1(1(1))，继续向外找到 0(1(1(0(1(1(1)))))+1(1(0(1(1(1))))))<del style="font-weight: bold; text-decoration: none;">，进行迭代得到，0</del>(1(1(0(1(1(1)))))+1(1(0(1(1(0(1(1(1)))))+1(1(0(1(1(0(1(1(1)))))+1(1(<del style="font-weight: bold; text-decoration: none;">...</del>)))))))))<del style="font-weight: bold; text-decoration: none;">，然后放回原来的层，得到0</del>(0(1(1(1)))+0(1(1(0(1(1(1)))))+1(1(0(1(1(0(1(1(1))) +1(1(0(1(1(0(1(1(1)))))+1(1(<del style="font-weight: bold; text-decoration: none;">..</del>))))))))))</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>p1 向外找到 <ins style="font-weight: bold; text-decoration: none;">&lt;math&gt;</ins>0(1(1(1))<ins style="font-weight: bold; text-decoration: none;">)&lt;/math&gt;</ins>，继续向外找到 <ins style="font-weight: bold; text-decoration: none;">&lt;math&gt;</ins>0(1(1(0(1(1(1)))))+1(1(0(1(1(1))))))<ins style="font-weight: bold; text-decoration: none;">&lt;/math&gt;，进行迭代得到 &lt;math&gt;0</ins>(1(1(0(1(1(1)))))+1(1(0(1(1(0(1(1(1)))))+1(1(0(1(1(0(1(1(1)))))+1(1(<ins style="font-weight: bold; text-decoration: none;">\dots</ins>)))))))))<ins style="font-weight: bold; text-decoration: none;">&lt;/math&gt;，然后放回原来的层，得到 &lt;math&gt;0</ins>(0(1(1(1)))+0(1(1(0(1(1(1)))))+1(1(0(1(1(0(1(1(1))) +1(1(0(1(1(0(1(1(1)))))+1(1(<ins style="font-weight: bold; text-decoration: none;">\dots</ins>))))))))))<ins style="font-weight: bold; text-decoration: none;">&lt;/math&gt;</ins></div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>M 记号还可以进一步扩展，得到 0(0(1(1(2(2(3(3(<del style="font-weight: bold; text-decoration: none;">...</del>)))))))) 或者 0(0(1(2(3(<del style="font-weight: bold; text-decoration: none;">...</del>)))) 或者 0(0(<del style="font-weight: bold; text-decoration: none;">ω</del>)) 的形式，其极限为 <del style="font-weight: bold; text-decoration: none;">ψ</del>(1-<del style="font-weight: bold; text-decoration: none;">α</del>.<del style="font-weight: bold; text-decoration: none;">Ω_(α</del>+2<del style="font-weight: bold; text-decoration: none;">)</del>-<del style="font-weight: bold; text-decoration: none;">Π1</del>)（此处为 pfec 稳定）=[[BGO]]。而另一种方向扩展的 LMN 可以更强，能够达到 BMS 的 (0)(1,1,1)(2,2,2)（[[LRO|pLRO]]）。</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>M 记号还可以进一步扩展，得到 <ins style="font-weight: bold; text-decoration: none;">&lt;math&gt;</ins>0(0(1(1(2(2(3(3(<ins style="font-weight: bold; text-decoration: none;">\dots</ins>))))))))<ins style="font-weight: bold; text-decoration: none;">&lt;/math&gt; </ins>或者 <ins style="font-weight: bold; text-decoration: none;">&lt;math&gt;</ins>0(0(1(2(3(<ins style="font-weight: bold; text-decoration: none;">\dots)</ins>))))<ins style="font-weight: bold; text-decoration: none;">&lt;/math&gt; </ins>或者 <ins style="font-weight: bold; text-decoration: none;">&lt;math&gt;</ins>0(0(<ins style="font-weight: bold; text-decoration: none;">\omega</ins>))<ins style="font-weight: bold; text-decoration: none;">&lt;/math&gt; </ins>的形式，其极限为 <ins style="font-weight: bold; text-decoration: none;">&lt;math&gt;\psi</ins>(1-<ins style="font-weight: bold; text-decoration: none;">\alpha</ins>.<ins style="font-weight: bold; text-decoration: none;">\Omega_{\alpha</ins>+2<ins style="font-weight: bold; text-decoration: none;">}</ins>-<ins style="font-weight: bold; text-decoration: none;">\Pi_1</ins>)<ins style="font-weight: bold; text-decoration: none;">&lt;/math&gt;</ins>（此处为 pfec 稳定）=[[BGO]]。而另一种方向扩展的 LMN 可以更强，能够达到 BMS 的 <ins style="font-weight: bold; text-decoration: none;">&lt;math&gt;</ins>(0)(1,1,1)(2,2,2)<ins style="font-weight: bold; text-decoration: none;">&lt;/math&gt;</ins>（[[LRO|pLRO]]）。</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[分类:重要概念]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[分类:重要概念]]</div></td></tr> <!-- diff cache key my_wiki:diff:1.41:old-2534:rev-2910:php=table --> </table>

星汐镜Littlekk http://wiki.googology.top/index.php?title=Dropping&diff=2534&oldid=prev 2025-08-28T05:52:40Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="zh-Hans-CN"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">←上一版本</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">2025年8月28日 (四) 13:52的版本</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l17">第17行：</td> <td colspan="2" class="diff-lineno">第17行：</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>M 记号还可以进一步扩展，得到 0(0(1(1(2(2(3(3(...)))))))) 或者 0(0(1(2(3(...)))) 或者 0(0(ω)) 的形式，其极限为 ψ(1-α.Ω_(α+2)-Π1)（此处为 pfec 稳定）=[[BGO]]。而另一种方向扩展的 LMN 可以更强，能够达到 BMS 的 (0)(1,1,1)(2,2,2)（[[LRO|pLRO]]）。</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>M 记号还可以进一步扩展，得到 0(0(1(1(2(2(3(3(...)))))))) 或者 0(0(1(2(3(...)))) 或者 0(0(ω)) 的形式，其极限为 ψ(1-α.Ω_(α+2)-Π1)（此处为 pfec 稳定）=[[BGO]]。而另一种方向扩展的 LMN 可以更强，能够达到 BMS 的 (0)(1,1,1)(2,2,2)（[[LRO|pLRO]]）。</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[[分类:重要概念]]</ins></div></td></tr> </table>

Z http://wiki.googology.top/index.php?title=Dropping&diff=1969&oldid=prev 2025-08-17T02:34:42Z

<p>创建页面，内容为“Dropping 模式是指在 <a href="/index.php/Kirby-Paris_Hydra" title="Kirby-Paris Hydra">Hydra</a> 中，往外找 n-Dropping 对应的 n 层的模式。 === M 记号 === M 记号实际上使用的是 2-dropping hydra 模式，而一般的 hydra 实际上是 1-dropping hydra。 比如 p0(p1+p1)，p1 向外找到 p0，然后进行迭代，得到 p0(p1+p0(p1+p0(p1+..)) 而在 M 记号中 p0(p0(p1)+p0(p1)，p1 向往找到等级更低的 p0，得到 p0(p1)，将其作为迭代子，继续向外找，得到…”</p> <p><b>新页面</b></p><div>Dropping 模式是指在 [[Kirby-Paris Hydra|Hydra]] 中，往外找 n-Dropping 对应的 n 层的模式。<br /> <br /> === M 记号 ===<br /> M 记号实际上使用的是 2-dropping hydra 模式，而一般的 hydra 实际上是 1-dropping hydra。<br /> <br /> 比如 p0(p1+p1)，p1 向外找到 p0，然后进行迭代，得到 p0(p1+p0(p1+p0(p1+..))<br /> <br /> 而在 M 记号中 p0(p0(p1)+p0(p1)，p1 向往找到等级更低的 p0，得到 p0(p1)，将其作为迭代子，继续向外找，得到，p0(p0(p1)+...)，然后进行迭代得到p0(p0(p1)+p0(p0(p1)+p0(p0(p1)+...))。p1 实际上是 p_1(0)，像 [[序数坍缩函数#BOCF 简介|BOCF]] 中 ψ_1(0)=Ω 一样，可以有 p_1(0)=M，进一步还有 p_1(p_1(0)=M^2,p_1(p_1(p_1(0))=M^M 这样，就能得到一般使用的 M 记号了。<br /> <br /> 以下省略 p：<br /> <br /> 0(0(1(1(1))+0(1(1(1))：首先是最右边的 p1 向外找到等级更低的 0(1(1(1))，继续向外找到等级更低的 0(0(1(1(1))+...))，而 0(1(1(1))&gt;0(1(1(0))&gt;0(0(1(1(1))+....)，于是进行补层，得到 0(1(1(0(1(1(1))+0(1(1(1))))，进行迭代得到，0(1(1(0(1(1(1))+0(1(1(0(1(1(1))+0(1(1(0(1(1(1))+...)))))))))，放回原来的层，得到 0(0(1(1(1))+0(1(1(0(1(1(1))+0(1(1(0(1(1(1)) +0(1(1(0(1(1(1))+...))))))))))<br /> <br /> 0(0(1(1(1)))+0(1(1(0(1(1(1)))))+1(1(0(1(1(1)))))))<br /> <br /> p1 向外找到 0(1(1(1))，继续向外找到 0(1(1(0(1(1(1)))))+1(1(0(1(1(1))))))，进行迭代得到，0(1(1(0(1(1(1)))))+1(1(0(1(1(0(1(1(1)))))+1(1(0(1(1(0(1(1(1)))))+1(1(...)))))))))，然后放回原来的层，得到0(0(1(1(1)))+0(1(1(0(1(1(1)))))+1(1(0(1(1(0(1(1(1))) +1(1(0(1(1(0(1(1(1)))))+1(1(..))))))))))<br /> <br /> M 记号还可以进一步扩展，得到 0(0(1(1(2(2(3(3(...)))))))) 或者 0(0(1(2(3(...)))) 或者 0(0(ω)) 的形式，其极限为 ψ(1-α.Ω_(α+2)-Π1)（此处为 pfec 稳定）=[[BGO]]。而另一种方向扩展的 LMN 可以更强，能够达到 BMS 的 (0)(1,1,1)(2,2,2)（[[LRO|pLRO]]）。</div>

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