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阿克曼函数 - 版本历史
2026-04-22T16:08:59Z
本wiki上该页面的版本历史
MediaWiki 1.43.1
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Zhy137036：/* Buck 的定义 */
2026-03-02T02:10:19Z
<p><span class="autocomment">Buck 的定义</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2日 (一) 10:10的版本</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l101">第101行：</td>
<td colspan="2" class="diff-lineno">第101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>但边界值略有不同：</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>但边界值略有不同：</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><math>\begin{aligned}F(0,y)&<del style="font-weight: bold; text-decoration: none;">=</del>\,y+1\\F(1,0)&<del style="font-weight: bold; text-decoration: none;">=</del>\,2\\F(2,0)&<del style="font-weight: bold; text-decoration: none;">=</del>\,0\\F(x,0)&<del style="font-weight: bold; text-decoration: none;">=</del>\,1\,\text{for }x=<del style="font-weight: bold; text-decoration: none;">\,</del>3,4,\cdots\end{aligned}</math></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><math>\begin{aligned}F(0,y)&\,<ins style="font-weight: bold; text-decoration: none;">=</ins>y+1\\F(1,0)&\,<ins style="font-weight: bold; text-decoration: none;">=</ins>2\\F(2,0)&\,<ins style="font-weight: bold; text-decoration: none;">=</ins>0\\F(x,0)&\,<ins style="font-weight: bold; text-decoration: none;">=</ins>1\,\text{for }x=3,4,\cdots\end{aligned}</math></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>这个函数递归得到：</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>这个函数递归得到：</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><math>\begin{aligned}F(1,y)&<del style="font-weight: bold; text-decoration: none;">=</del>\,2+y\\F(2,y)&<del style="font-weight: bold; text-decoration: none;">=</del>\,2y\\F(3,y)&<del style="font-weight: bold; text-decoration: none;">=</del>\,2^y\\F(4,y)&<del style="font-weight: bold; text-decoration: none;">=</del>\,2\uparrow\uparrow y\end{aligned}</math></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><math>\begin{aligned}F(1,y)&\,<ins style="font-weight: bold; text-decoration: none;">=</ins>2+y\\F(2,y)&\,<ins style="font-weight: bold; text-decoration: none;">=</ins>2y\\F(3,y)&\,<ins style="font-weight: bold; text-decoration: none;">=</ins>2^y\\F(4,y)&\,<ins style="font-weight: bold; text-decoration: none;">=</ins>2\uparrow\uparrow y\end{aligned}</math></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>F(4,n) 给出了序列 1, 2, 4, 16, 65536, 2<sup>65536</sup>,... (OEIS [http://oeis.org/A014221 A014221])；</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>F(4,n) 给出了序列 1, 2, 4, 16, 65536, 2<sup>65536</sup>,... (OEIS [http://oeis.org/A014221 A014221])；</div></td></tr>
</table>
Zhy137036
http://wiki.googology.top/index.php?title=%E9%98%BF%E5%85%8B%E6%9B%BC%E5%87%BD%E6%95%B0&diff=2916&oldid=prev
Phyrion：美化公式
2026-03-01T19:21:52Z
<p>美化公式</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2日 (一) 03:21的版本</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l101">第101行：</td>
<td colspan="2" class="diff-lineno">第101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>但边界值略有不同：</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>但边界值略有不同：</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><math>\begin{aligned}F(0,y)&=\,y+1\\F(1,0)&=\,2\\F(2,0)&=\,0\\F(x,0)&=\,1\text{for }x=\,3,4,\cdots\end{aligned}</math></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><math>\begin{aligned}F(0,y)&=\,y+1\\F(1,0)&=\,2\\F(2,0)&=\,0\\F(x,0)&=\,1<ins style="font-weight: bold; text-decoration: none;">\,</ins>\text{for }x=\,3,4,\cdots\end{aligned}</math></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>这个函数递归得到：</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>这个函数递归得到：</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><math>\begin{aligned}F(1,y)&=2+y\\F(2,y)&=2y\\F(3,y)&=2^y\\F(4,y)&=2\uparrow\uparrow y\end{aligned}</math></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><math>\begin{aligned}F(1,y)&=<ins style="font-weight: bold; text-decoration: none;">\,</ins>2+y\\F(2,y)&=<ins style="font-weight: bold; text-decoration: none;">\,</ins>2y\\F(3,y)&=<ins style="font-weight: bold; text-decoration: none;">\,</ins>2^y\\F(4,y)&=<ins style="font-weight: bold; text-decoration: none;">\,</ins>2\uparrow\uparrow y\end{aligned}</math></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>F(4,n) 给出了序列 1, 2, 4, 16, 65536, 2<sup>65536</sup>,... (OEIS [http://oeis.org/A014221 A014221])；</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>F(4,n) 给出了序列 1, 2, 4, 16, 65536, 2<sup>65536</sup>,... (OEIS [http://oeis.org/A014221 A014221])；</div></td></tr>
</table>
Phyrion
http://wiki.googology.top/index.php?title=%E9%98%BF%E5%85%8B%E6%9B%BC%E5%87%BD%E6%95%B0&diff=2915&oldid=prev
2026年3月1日 (日) 19:21 Phyrion
2026-03-01T19:21:01Z
<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;">2026年3月2日 (一) 03:21的版本</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l101">第101行：</td>
<td colspan="2" class="diff-lineno">第101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>但边界值略有不同：</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>但边界值略有不同：</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><math>\begin{aligned}F(0,y)&=y+1\\F(1,0)&=2\\F(2,0)&=0\\F(x,0)&=1\text{for }x=3,4,\cdots\end{aligned}</math></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><math>\begin{aligned}F(0,y)&=<ins style="font-weight: bold; text-decoration: none;">\,</ins>y+1\\F(1,0)&=<ins style="font-weight: bold; text-decoration: none;">\,</ins>2\\F(2,0)&=<ins style="font-weight: bold; text-decoration: none;">\,</ins>0\\F(x,0)&=<ins style="font-weight: bold; text-decoration: none;">\,</ins>1\text{for }x=<ins style="font-weight: bold; text-decoration: none;">\,</ins>3,4,\cdots\end{aligned}</math></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>这个函数递归得到：</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>这个函数递归得到：</div></td></tr>
</table>
Phyrion
http://wiki.googology.top/index.php?title=%E9%98%BF%E5%85%8B%E6%9B%BC%E5%87%BD%E6%95%B0&diff=2914&oldid=prev
Phyrion：/* Buck 的定义 */
2026-03-01T19:18:26Z
<p><span class="autocomment">Buck 的定义</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2日 (一) 03:18的版本</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l101">第101行：</td>
<td colspan="2" class="diff-lineno">第101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>但边界值略有不同：</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>但边界值略有不同：</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><math>\begin{<del style="font-weight: bold; text-decoration: none;">align</del>}F(0,y)&=<del style="font-weight: bold; text-decoration: none;">&</del>y+1<del style="font-weight: bold; text-decoration: none;">&</del>\\F(1,0)&=<del style="font-weight: bold; text-decoration: none;">&</del>2<del style="font-weight: bold; text-decoration: none;">&</del>\\F(2,0)&=<del style="font-weight: bold; text-decoration: none;">&</del>0<del style="font-weight: bold; text-decoration: none;">&</del>\\F(x,0)&=<del style="font-weight: bold; text-decoration: none;">&</del>1<del style="font-weight: bold; text-decoration: none;">&</del>\text{for }x=3,4,\cdots\end{<del style="font-weight: bold; text-decoration: none;">align</del>}</math></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><math>\begin{<ins style="font-weight: bold; text-decoration: none;">aligned</ins>}F(0,y)&=y+1\\F(1,0)&=2\\F(2,0)&=0\\F(x,0)&=1\text{for }x=3,4,\cdots\end{<ins style="font-weight: bold; text-decoration: none;">aligned</ins>}</math></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>这个函数递归得到：</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>这个函数递归得到：</div></td></tr>
</table>
Phyrion
http://wiki.googology.top/index.php?title=%E9%98%BF%E5%85%8B%E6%9B%BC%E5%87%BD%E6%95%B0&diff=2913&oldid=prev
Phyrion：/* Buck 的定义 */
2026-03-01T19:17:32Z
<p><span class="autocomment">Buck 的定义</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2日 (一) 03:17的版本</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l101">第101行：</td>
<td colspan="2" class="diff-lineno">第101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>但边界值略有不同：</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>但边界值略有不同：</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><math>\begin{<del style="font-weight: bold; text-decoration: none;">aligned</del>}F(0,y)&=&y+1&\\F(1,0)&=&2&\\F(2,0)&=&0&\\F(x,0)&=&1&\text{for }x=3,4,\cdots\end{<del style="font-weight: bold; text-decoration: none;">aligned</del>}</math></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><math>\begin{<ins style="font-weight: bold; text-decoration: none;">align</ins>}F(0,y)&=&y+1&\\F(1,0)&=&2&\\F(2,0)&=&0&\\F(x,0)&=&1&\text{for }x=3,4,\cdots\end{<ins style="font-weight: bold; text-decoration: none;">align</ins>}</math></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>这个函数递归得到：</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>这个函数递归得到：</div></td></tr>
</table>
Phyrion
http://wiki.googology.top/index.php?title=%E9%98%BF%E5%85%8B%E6%9B%BC%E5%87%BD%E6%95%B0&diff=2912&oldid=prev
Phyrion：美化排版
2026-03-01T19:16:48Z
<p>美化排版</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2日 (一) 03:16的版本</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l105">第105行：</td>
<td colspan="2" class="diff-lineno">第105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>这个函数递归得到：</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>这个函数递归得到：</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><math>\begin{aligned}F(1,y)&=<del style="font-weight: bold; text-decoration: none;">&</del>2+y\\F(2,y)&=<del style="font-weight: bold; text-decoration: none;">&</del>2y\\F(3,y)&=<del style="font-weight: bold; text-decoration: none;">&</del>2^y\\F(4,y)&=<del style="font-weight: bold; text-decoration: none;">&</del>2\uparrow\uparrow y\end{aligned}</math></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><math>\begin{aligned}F(1,y)&=2+y\\F(2,y)&=2y\\F(3,y)&=2^y\\F(4,y)&=2\uparrow\uparrow y\end{aligned}</math></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>F(4,n) 给出了序列 1, 2, 4, 16, 65536, 2<sup>65536</sup>,... (OEIS [http://oeis.org/A014221 A014221])；</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>F(4,n) 给出了序列 1, 2, 4, 16, 65536, 2<sup>65536</sup>,... (OEIS [http://oeis.org/A014221 A014221])；</div></td></tr>
</table>
Phyrion
http://wiki.googology.top/index.php?title=%E9%98%BF%E5%85%8B%E6%9B%BC%E5%87%BD%E6%95%B0&diff=2911&oldid=prev
Phyrion：/* 示例 */
2026-03-01T19:14:00Z
<p><span class="autocomment">示例</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2日 (一) 03:14的版本</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l12">第12行：</td>
<td colspan="2" class="diff-lineno">第12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>==== 示例 ====</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>==== 示例 ====</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><math>\begin{array}{lll}</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><math>\begin{array}{lll}</div></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>A(2,2) &=<del style="font-weight: bold; text-decoration: none;">& </del>A(1,A(2,1))\\ &=<del style="font-weight: bold; text-decoration: none;">& </del>A(1,A(1,A(2,0)))<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>A(2,2) &= A(1,A(2,1))\\ &= A(1,A(1,A(2,0)))\\</div></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> &=<del style="font-weight: bold; text-decoration: none;">& </del>A(1,A(1,A(1,1)))\\ &=<del style="font-weight: bold; text-decoration: none;">& </del>A(1,A(1,A(0,A(1,0))))\\ &=<del style="font-weight: bold; text-decoration: none;">& </del> A(1,A(1,A(0,A(0,1))))\\ &=<del style="font-weight: bold; text-decoration: none;">& </del>A(1,A(1,A(0,2)))\\&=<del style="font-weight: bold; text-decoration: none;">& </del>A(1, A(1, 3))\\</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> &= A(1,A(1,A(1,1)))\\ &= A(1,A(1,A(0,A(1,0))))\\ &= A(1,A(1,A(0,A(0,1))))\\ &= A(1,A(1,A(0,2)))\\&= A(1, A(1, 3))\\</div></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>&=<del style="font-weight: bold; text-decoration: none;">& </del>A(1, A(0, A(1, 2)))\\ &=<del style="font-weight: bold; text-decoration: none;">& </del>A(1, A(0, A(0, A(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>&= A(1, A(0, A(1, 2)))\\ &= A(1, A(0, A(0, A(1, 1))))\\</div></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>&=<del style="font-weight: bold; text-decoration: none;">& </del>A(1, A(0, A(0, A(0, A(1, 0)))))\\ &=<del style="font-weight: bold; text-decoration: none;">& </del>A(1, A(0, A(0, A(0, A(0, 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>&= A(1, A(0, A(0, A(0, A(1, 0)))))\\ &= A(1, A(0, A(0, A(0, A(0, 1)))))\\</div></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>&=<del style="font-weight: bold; text-decoration: none;">& </del>A(1, A(0, A(0, A(0, 2))))\\</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>&= A(1, A(0, A(0, A(0, 2))))\\</div></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>&=<del style="font-weight: bold; text-decoration: none;">& </del>A(1, A(0, A(0, 3)))\\ &=<del style="font-weight: bold; text-decoration: none;">& </del>A(1, A(0, 4))\\ &=<del style="font-weight: bold; text-decoration: none;">& </del>A(1, 5)\\ &=<del style="font-weight: bold; text-decoration: none;">& </del>A(0, A(1, 4))\\</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>&= A(1, A(0, A(0, 3)))\\ &= A(1, A(0, 4))\\ &= A(1, 5)\\ &= A(0, A(1, 4))\\</div></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>&=<del style="font-weight: bold; text-decoration: none;">& </del>A(0, A(0, A(1, 3)))\\ &=<del style="font-weight: bold; text-decoration: none;">& </del>A(0, A(0, A(0, A(1, 2))))\\</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>&= A(0, A(0, A(1, 3)))\\ &= A(0, A(0, A(0, A(1, 2))))\\</div></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>&=<del style="font-weight: bold; text-decoration: none;">& </del>A(0, A(0, A(0, A(0, A(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>&= A(0, A(0, A(0, A(0, A(1, 1)))))\\</div></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>&=<del style="font-weight: bold; text-decoration: none;">& </del>A(0, A(0, A(0, A(0, A(0, A(1, 0))))))\\</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>&= A(0, A(0, A(0, A(0, A(0, A(1, 0))))))\\</div></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>&=<del style="font-weight: bold; text-decoration: none;">& </del>A(0, A(0, A(0, A(0, A(0, A(0, 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>&= A(0, A(0, A(0, A(0, A(0, A(0, 1))))))\\</div></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>&=<del style="font-weight: bold; text-decoration: none;">& </del>A(0, A(0, A(0, A(0, A(0, 2)))))\\ &=<del style="font-weight: bold; text-decoration: none;">& </del>A(0, A(0, A(0, A(0, 3))))\\</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>&= A(0, A(0, A(0, A(0, A(0, 2)))))\\ &= A(0, A(0, A(0, A(0, 3))))\\</div></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>&=<del style="font-weight: bold; text-decoration: none;">& </del>A(0, A(0, A(0, 4)))\\ &=<del style="font-weight: bold; text-decoration: none;">& </del>A(0, A(0, 5))\\ &=<del style="font-weight: bold; text-decoration: none;">& </del>A(0, 6)\\ &=<del style="font-weight: bold; text-decoration: none;">& </del>7</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>&= A(0, A(0, A(0, 4)))\\ &= A(0, A(0, 5))\\ &= A(0, 6)\\ &= 7</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>\end{array}</math></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>\end{array}</math></div></td></tr>
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Phyrion
http://wiki.googology.top/index.php?title=%E9%98%BF%E5%85%8B%E6%9B%BC%E5%87%BD%E6%95%B0&diff=2148&oldid=prev
2025年8月20日 (三) 08:27 Z
2025-08-20T08:27:23Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">2025年8月20日 (三) 16:27的版本</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l147">第147行：</td>
<td colspan="2" class="diff-lineno">第147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>——Alistair Cockburn</blockquote>函数 <math>A(x)=A(x,x)</math>（基于 Robinson 定义）是阿克曼函数的对角化，这个函数也被叫做 Gag 或 Knackeredman。这个名字来自 Alistair Cockburn，由于阿克曼函数与[[高德纳箭头|上箭头表示法]]的关系，<math>A(x)=2\uparrow^{x-2}(x+3)-3</math>。<ref>Gag | Googology Wiki, Cooperation, January 11, 2009. https://googology.fandom.com/wiki/Gag</ref></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>——Alistair Cockburn</blockquote>函数 <math>A(x)=A(x,x)</math>（基于 Robinson 定义）是阿克曼函数的对角化，这个函数也被叫做 Gag 或 Knackeredman。这个名字来自 Alistair Cockburn，由于阿克曼函数与[[高德纳箭头|上箭头表示法]]的关系，<math>A(x)=2\uparrow^{x-2}(x+3)-3</math>。<ref>Gag | Googology Wiki, Cooperation, January 11, 2009. https://googology.fandom.com/wiki/Gag</ref></div></td></tr>
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<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;">{{默认排序:大数记号}}</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;"><div>[[分类:记号]]</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:记号]]</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:入门]]</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:入门]]</div></td></tr>
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Z
http://wiki.googology.top/index.php?title=%E9%98%BF%E5%85%8B%E6%9B%BC%E5%87%BD%E6%95%B0&diff=1559&oldid=prev
2025年7月27日 (日) 09:08 Tabelog
2025-07-27T09:08:08Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">2025年7月27日 (日) 17:08的版本</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l144">第144行：</td>
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<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>==== 阿克曼函数的对角化 ====</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>==== 阿克曼函数的对角化 ====</div></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><del style="font-weight: bold; text-decoration: none;">函数 </del><<del style="font-weight: bold; text-decoration: none;">math</del>><del style="font-weight: bold; text-decoration: none;">A</del>(<del style="font-weight: bold; text-decoration: none;">x</del>)<del style="font-weight: bold; text-decoration: none;">=A</del>(<del style="font-weight: bold; text-decoration: none;">x</del>,<del style="font-weight: bold; text-decoration: none;">x</del>)<del style="font-weight: bold; text-decoration: none;"></math>（基于 Robinson 定义）是阿克曼函数的对角化，这个函数也被叫做 </del>Gag <del style="font-weight: bold; text-decoration: none;">或 Knackeredman。这个名字来自 Alistair Cockburn，由于阿克曼函数与[[高德纳箭头|上箭头表示法]]的关系，<math>A</del>(<del style="font-weight: bold; text-decoration: none;">x</del>)<del style="font-weight: bold; text-decoration: none;">=2\uparrow</del>^<del style="font-weight: bold; text-decoration: none;">{x-2}(x+3)-3</math>。<ref>Gag | Googology Wiki, Cooperation, January 11, 2009. https://googology.fandom.com/wiki/Gag</ref></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;">blockquote</ins>><ins style="font-weight: bold; text-decoration: none;">阿克曼函数让我有些困扰，因为它是一个二元函数，而我们更关注一元函数。显然，对于任意的 n，Ackermann</ins>(<ins style="font-weight: bold; text-decoration: none;">n,n) 应该有个特定的名称吧？比如 Knackered_Man(n</ins>) <ins style="font-weight: bold; text-decoration: none;">或者 Ackermann</ins>(<ins style="font-weight: bold; text-decoration: none;">n</ins>,<ins style="font-weight: bold; text-decoration: none;">n</ins>)<ins style="font-weight: bold; text-decoration: none;">？或者简称 </ins>Gag(<ins style="font-weight: bold; text-decoration: none;">n</ins>)<ins style="font-weight: bold; text-decoration: none;">？另外，像+、*、</ins>^<ins style="font-weight: bold; text-decoration: none;">这样的进阶运算……它们在递进过程中会生成新的函数吗？这就是所谓的 tetration 和 quintation 的意思吗？感谢解答这些疑问</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 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;">——Alistair Cockburn</blockquote>函数 <math>A(x)=A(x,x)</math>（基于 Robinson 定义）是阿克曼函数的对角化，这个函数也被叫做 Gag 或 Knackeredman。这个名字来自 Alistair Cockburn，由于阿克曼函数与[[高德纳箭头|上箭头表示法]]的关系，<math>A(x)=2\uparrow^{x-2}(x+3)-3</math>。<ref>Gag | Googology Wiki, Cooperation, January 11, 2009. https://googology.fandom.com/wiki/Gag</ref></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;"><div>[[分类:记号]]</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:记号]]</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:入门]]</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:入门]]</div></td></tr>
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Tabelog
http://wiki.googology.top/index.php?title=%E9%98%BF%E5%85%8B%E6%9B%BC%E5%87%BD%E6%95%B0&diff=857&oldid=prev
2025年7月6日 (日) 07:26 Phyrion
2025-07-06T07:26:41Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">2025年7月6日 (日) 15:26的版本</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l92">第92行：</td>
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<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>==== Friedman 的定义 ====</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>==== Friedman 的定义 ====</div></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><math>A(x,y)=\begin{cases}2&,y=1\\2y&,x=1\<del style="font-weight: bold; text-decoration: none;">land </del>y>1\\A(x-1,A(x,y-1))&,x>1\<del style="font-weight: bold; text-decoration: none;">land </del>y>1\end{cases}</math></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><math>A(x,y)=\begin{cases}2&,y=1\\2y&,x=1\ <ins style="font-weight: bold; text-decoration: none;">\text{and}\ </ins>y>1\\A(x-1,A(x,y-1))&,x>1\ <ins style="font-weight: bold; text-decoration: none;">\text{and}\ </ins>y>1\end{cases}</math></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>在这个定义下，<math>A(x,y)=2\uparrow^{x-1}y</math>。<ref>Harvey M. Friedman. THE ACKERMANN FUNCTION IN ELEMENTARY ALGEBRAIC GEOMETRY, October 21, 2000. https://cpb-us-w2.wpmucdn.com/u.osu.edu/dist/1/1952/files/2014/01/AckAlgGeom102100-1rrdkag.pdf</ref></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>在这个定义下，<math>A(x,y)=2\uparrow^{x-1}y</math>。<ref>Harvey M. Friedman. THE ACKERMANN FUNCTION IN ELEMENTARY ALGEBRAIC GEOMETRY, October 21, 2000. https://cpb-us-w2.wpmucdn.com/u.osu.edu/dist/1/1952/files/2014/01/AckAlgGeom102100-1rrdkag.pdf</ref></div></td></tr>
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Phyrion