| Number | SGH ordinal |
|---|---|
| \(0\) | \(0\) |
| \(1\) | \(1\) |
| \(2\) | \(\varepsilon_0\) |
| \(3\) | \(\varepsilon_0+1\) |
| \(4\) | \(\varepsilon_0^{\varepsilon_0}\) |
| \(5\) | \(\varepsilon_0^{\varepsilon_0}+1\) |
| \(6\) | \(\varepsilon_0^{\varepsilon_0}+\varepsilon_0\) |
| \(7\) | \(\varepsilon_0^{\varepsilon_0}+\varepsilon_0+1\) |
| \(8\) | \(\varepsilon_0^{\varepsilon_0+1}\) |
| \(10\) | \(\varepsilon_0^{\varepsilon_0+1}+\varepsilon_0\) |
| \(12\) | \(\varepsilon_0^{\varepsilon_0+1}+\varepsilon_0^{\varepsilon_0}\) |
| \(14\) | \(\varepsilon_0^{\varepsilon_0+1}+\varepsilon_0^{\varepsilon_0}+\varepsilon_0\) |
| \(16\) | \(\varepsilon_0^{\varepsilon_0^{\varepsilon_0}}\) |
| \(20\) | \(\varepsilon_0^{\varepsilon_0^{\varepsilon_0}}+\varepsilon_0^{\varepsilon_0}\) |
| \(24\) | \(\varepsilon_0^{\varepsilon_0^{\varepsilon_0}}+\varepsilon_0^{\varepsilon_0+1}\) |
| \(28\) | \(\varepsilon_0^{\varepsilon_0^{\varepsilon_0}}+\varepsilon_0^{\varepsilon_0+1}+\varepsilon_0^{\varepsilon_0}\) |
| \(32\) | \(\varepsilon_0^{\varepsilon_0^{\varepsilon_0}+1}\) |
| \(40\) | \(\varepsilon_0^{\varepsilon_0^{\varepsilon_0}+1}+\varepsilon_0^{\varepsilon_0+1}\) |
| \(48\) | \(\varepsilon_0^{\varepsilon_0^{\varepsilon_0}+1}+\varepsilon_0^{\varepsilon_0^{\varepsilon_0}}\) |
| \(56\) | \(\varepsilon_0^{\varepsilon_0^{\varepsilon_0}+1}+\varepsilon_0^{\varepsilon_0^{\varepsilon_0}}+\varepsilon_0^{\varepsilon_0+1}\) |
| \(64\) | \(\varepsilon_0^{\varepsilon_0^{\varepsilon_0}+\varepsilon_0}\) |
| \(128\) | \(\varepsilon_0^{\varepsilon_0^{\varepsilon_0}+\varepsilon_0+1}\) |
| \(256\) | \(\varepsilon_1\) |
| \(512\) | \(\varepsilon_1\varepsilon_0\) |
| \(1,024\) | \(\varepsilon_1\varepsilon_0^{\varepsilon_0}\) |
| \(2,048\) | \(\varepsilon_1\varepsilon_0^{\varepsilon_0+1}\) |
| \(4,096\) | \(\varepsilon_1\varepsilon_0^{\varepsilon_0^{\varepsilon_0}}\) |
| \(8,192\) | \(\varepsilon_1\varepsilon_0^{\varepsilon_0^{\varepsilon_0}+1}\) |
| \(16,384\) | \(\varepsilon_1\varepsilon_0^{\varepsilon_0^{\varepsilon_0}+\varepsilon_0}\) |
| \(32,768\) | \(\varepsilon_1\varepsilon_0^{\varepsilon_0^{\varepsilon_0}+\varepsilon_0+1}\) |
| \(65,536\) | \(\varepsilon_1^{\varepsilon_0}\) |
| \(2^{18}\) | \(\varepsilon_1^{\varepsilon_0}\varepsilon_0^{\varepsilon_0}\) |
| \(2^{20}\) | \(\varepsilon_1^{\varepsilon_0}\varepsilon_0^{\varepsilon_0^{\varepsilon_0}}\) |
| \(2^{22}\) | \(\varepsilon_1^{\varepsilon_0}\varepsilon_0^{\varepsilon_0^{\varepsilon_0}+\varepsilon_0}\) |
| \(2^{24}\) | \(\varepsilon_1^{\varepsilon_0+1}\) |
| \(2^{26}\) | \(\varepsilon_1^{\varepsilon_0+1}\varepsilon_0^{\varepsilon_0}\) |
| \(2^{28}\) | \(\varepsilon_1^{\varepsilon_0+1}\varepsilon_0^{\varepsilon_0^{\varepsilon_0}}\) |
| \(2^{30}\) | \(\varepsilon_1^{\varepsilon_0+1}\varepsilon_0^{\varepsilon_0^{\varepsilon_0}+\varepsilon_0}\) |
| \(2^{32}\) | \(\varepsilon_1^{\varepsilon_0^{\varepsilon_0}}\) |
| \(2^{40}\) | \(\varepsilon_1^{\varepsilon_0^{\varepsilon_0}+1}\) |
| \(2^{48}\) | \(\varepsilon_1^{\varepsilon_0^{\varepsilon_0}+\varepsilon_0}\) |
| \(2^{64}\) | \(\varepsilon_1^{\varepsilon_0^{\varepsilon_0+1}}\) |
| \(2^{80}\) | \(\varepsilon_1^{\varepsilon_0^{\varepsilon_0+1}+\varepsilon_0}\) |
| \(2^{96}\) | \(\varepsilon_1^{\varepsilon_0^{\varepsilon_0+1}+\varepsilon_0^{\varepsilon_0}}\) |
| \(2^{112}\) | \(\varepsilon_1^{\varepsilon_0^{\varepsilon_0+1}+\varepsilon_0^{\varepsilon_0}+\varepsilon_0}\) |
| \(2^{128}\) | \(\varepsilon_1^{\varepsilon_0^{\varepsilon_0^{\varepsilon_0}}}\) |
| \(2^{192}\) | \(\varepsilon_1^{\varepsilon_0^{\varepsilon_0^{\varepsilon_0}}+1}\) |
| \(2^{256}\) | \(\varepsilon_1^{\varepsilon_1}\) |
| \(2^{1,024}\) | \(\varepsilon_1^{\varepsilon_1\varepsilon_0^{\varepsilon_0}}\) |
| \(2^{4,096}\) | \(\varepsilon_1^{\varepsilon_1\varepsilon_0^{\varepsilon_0^{\varepsilon_0}}}\) |
| \(2^{16,384}\) | \(\varepsilon_1^{\varepsilon_1\varepsilon_0^{\varepsilon_0^{\varepsilon_0}+1}}\) |
| \(2^{65,536}\) | \(\varepsilon_1^{\varepsilon_1^{\varepsilon_1}}\) |
| \(2^{2^{17}}\) | \(\varepsilon_{\varepsilon_0}\) |
| \(2^{2^{18}}\) | \(\varepsilon_{\varepsilon_0}^{\varepsilon_0}\) |
| \(2^{2^{32}}\) | \(\varepsilon_{\varepsilon_0}^{\varepsilon_0^{\varepsilon_0}}\) |
| \(2^{2^{48}}\) | \(\varepsilon_{\varepsilon_0}^{\varepsilon_0^{\varepsilon_0^{\varepsilon_0}+1}}\) |
| \(2^{2^{80}}\) | \(\varepsilon_{\varepsilon_0}^{\varepsilon_0^{\varepsilon_0^{\varepsilon_0}+\varepsilon_0}}\) |
| \(2^{2^{144}}\) | \(\varepsilon_{\varepsilon_0}^{\varepsilon_0^{\varepsilon_0^{\varepsilon_0}+\varepsilon_0+1}}\) |
| \(2^{2^{272}}\) | \(\varepsilon_{\varepsilon_0}^{\varepsilon_1}\) |
| \(2^{2^{1,040}}\) | \(\varepsilon_{\varepsilon_0}^{\varepsilon_1\varepsilon_0^{\varepsilon_0}}\) |
| \(2^{2^{4,112}}\) | \(\varepsilon_{\varepsilon_0}^{\varepsilon_1\varepsilon_0^{\varepsilon_0^{\varepsilon_0}}}\) |
| \(2^{2^{16,400}}\) | \(\varepsilon_{\varepsilon_0}^{\varepsilon_1\varepsilon_0^{\varepsilon_0^{\varepsilon_0}+\varepsilon_0}}\) |
| \(2^{2^{65,552}}\) | \(\varepsilon_{\varepsilon_0}^{\varepsilon_1^{\varepsilon_0}}\) |
| \(2^{2^{2^{20}+16}}\) | \(\varepsilon_{\varepsilon_0}^{\varepsilon_1^{\varepsilon_0}\varepsilon_0^{\varepsilon_0^{\varepsilon_0}}}\) |
| \(2^{2^{2^{24}+16}}\) | \(\varepsilon_{\varepsilon_0}^{\varepsilon_1^{\varepsilon_0+1}}\) |
| \(2^{2^{2^{28}+16}}\) | \(\varepsilon_{\varepsilon_0}^{\varepsilon_1^{\varepsilon_0+1}\varepsilon_0^{\varepsilon_0^{\varepsilon_0}}}\) |
| \(2^{2^{2^{32}+16}}\) | \(\varepsilon_{\varepsilon_0}^{\varepsilon_1^{\varepsilon_0^{\varepsilon_0}}}\) |
| \(2^{2^{2^{64}+16}}\) | \(\varepsilon_{\varepsilon_0}^{\varepsilon_1^{\varepsilon_0^{\varepsilon_0+1}}}\) |
| \(2^{2^{2^{128}+16}}\) | \(\varepsilon_{\varepsilon_0}^{\varepsilon_1^{\varepsilon_0^{\varepsilon_0^{\varepsilon_0}}}}\) |
| \(2^{2^{2^{256}+16}}\) | \(\varepsilon_{\varepsilon_0}^{\varepsilon_1^{\varepsilon_1}}\) |
| \(2^{2^{2^{4,096}+16}}\) | \(\varepsilon_{\varepsilon_0}^{\varepsilon_1^{\varepsilon_1\varepsilon_0^{\varepsilon_0^{\varepsilon_0}}}}\) |
| \(2^{2^{2^{65,536}+16}}\) | \(\varepsilon_{\varepsilon_0}^{\varepsilon_1^{\varepsilon_1^{\varepsilon_1}}}\) |
| \(2^{2^{2^{2^{17}}+16}}\) | \(\varepsilon_{\varepsilon_0}^{\varepsilon_{\varepsilon_0}}\) |
| \(2^{2^{2^{2^{32}}+16}}\) | \(\varepsilon_{\varepsilon_0}^{\varepsilon_{\varepsilon_0}^{\varepsilon_0^{\varepsilon_0}}}\) |
| \(2^{2^{2^{2^{144}}+16}}\) | \(\varepsilon_{\varepsilon_0}^{\varepsilon_{\varepsilon_0}^{\varepsilon_0^{\varepsilon_0^{\varepsilon_0}+\varepsilon_0+1}}}\) |
| \(2^{2^{2^{2^{1,040}}+16}}\) | \(\varepsilon_{\varepsilon_0}^{\varepsilon_{\varepsilon_0}^{\varepsilon_1\varepsilon_0^{\varepsilon_0}}}\) |
| \(2^{2^{2^{2^{65,552}}+16}}\) | \(\varepsilon_{\varepsilon_0}^{\varepsilon_{\varepsilon_0}^{\varepsilon_1^{\varepsilon_0}}}\) |
| \(2^{2^{2^{2^{2^{24}+16}}+16}}\) | \(\varepsilon_{\varepsilon_0}^{\varepsilon_{\varepsilon_0}^{\varepsilon_1^{\varepsilon_0+1}}}\) |
| \(2^{2^{2^{2^{2^{64}+16}}+16}}\) | \(\varepsilon_{\varepsilon_0}^{\varepsilon_{\varepsilon_0}^{\varepsilon_1^{\varepsilon_0^{\varepsilon_0+1}}}}\) |
| \(2^{2^{2^{2^{2^{2^{17}}+16}}+16}}\) | \(\varepsilon_{\varepsilon_0+1}\) |
| Wall of | Approximation |
| \((2\uparrow)^617\) | \(\varepsilon_{\varepsilon_0+1}\) |
| \((2\uparrow)^765,552\) | \(\varepsilon_{\varepsilon_0+1}^{\varepsilon_1^{\varepsilon_0}}\) |
| \((2\uparrow)^865,536\) | \(\varepsilon_{\varepsilon_0+1}^{\varepsilon_1^{\varepsilon_1^{\varepsilon_1}}}\) |
| \((2\uparrow)^965,552\) | \(\varepsilon_{\varepsilon_0+1}^{\varepsilon_{\varepsilon_0}^{\varepsilon_1^{\varepsilon_0}}}\) |
| \((2\uparrow)^{10}65,536\) | \(\varepsilon_{\varepsilon_0+1}^{\varepsilon_{\varepsilon_0}^{\varepsilon_1^{\varepsilon_1^{\varepsilon_1}}}}\) |
| \((2\uparrow)^{12}65,536\) | \(\varepsilon_{\varepsilon_0+1}^{\varepsilon_{\varepsilon_0}^{\varepsilon_{\varepsilon_0}^{\varepsilon_1^{\varepsilon_1^{\varepsilon_1}}}}}\) |
| \((2\uparrow)^{14}65,536\) | \(\varepsilon_{\varepsilon_0+1}^{\varepsilon_{\varepsilon_0+1}^{\varepsilon_{\varepsilon_0}^{\varepsilon_1^{\varepsilon_1^{\varepsilon_1}}}}}\) |
| \((2\uparrow)^{18}17\) | \(\varepsilon_{\varepsilon_0^{\varepsilon_0}}\) |
| \((2\uparrow)^{26}17\) | \(\varepsilon_{\varepsilon_0^{\varepsilon_0}}^{\varepsilon_{\varepsilon_0+1}^{\zeta_0}}\) |
| \((2\uparrow)^{54}17\) | \(\varepsilon_{\varepsilon_0^{\varepsilon_0}+1}\) |
| \((2\uparrow)^{162}17\) | \(\varepsilon_{\varepsilon_0^{\varepsilon_0}+\varepsilon_0}\) |
| \((2\uparrow)^{1,458}17\) | \(\varepsilon_{\varepsilon_0^{\varepsilon_0+1}}\) |
| \((2\uparrow)^{3^{14}2}17\) | \(\varepsilon_{\varepsilon_0^{\varepsilon_0^{\varepsilon_0}}}\) |
| \((2\uparrow)^{3^{254}2}17\) | \(\varepsilon_{\varepsilon_1}\) |
| \((2\uparrow)^{3^{2^{2^{17}}-2}2}17\) | \(\zeta_0\lbrack3\rbrack\) |
| \(2\uparrow\uparrow2\uparrow\uparrow3^{2^{2^{17}}}\) | \(\zeta_1\) |
| \(2\uparrow\uparrow2\uparrow\uparrow2\uparrow\uparrow3^{2^{2^{17}}}\) | \(\varepsilon_{\zeta_1+1}\) |
| \((2\uparrow\uparrow)^43^{2^{2^{17}}}\) | \(\zeta_{\varepsilon_0}\) |
| \((2\uparrow\uparrow)^63^{2^{2^{17}}}\) | \(\zeta_{\varepsilon_0+1}\) |
| \((2\uparrow\uparrow)^83^{2^{2^{17}}}\) | \(\zeta_{\varepsilon_0^{\varepsilon_0}}\) |
| \((2\uparrow\uparrow)^{16}3^{2^{2^{17}}}\) | \(\zeta_{\varepsilon_0^{\varepsilon_0+1}}\) |
| \((2\uparrow\uparrow)^{32}3^{2^{2^{17}}}\) | \(\zeta_{\varepsilon_0^{\varepsilon_0^{\varepsilon_0}}}\) |
| \((2\uparrow\uparrow)^{512}3^{2^{2^{17}}}\) | \(\zeta_{\varepsilon_1}\) |
| \((2\uparrow\uparrow)^{2^{257}}3^{2^{2^{17}}}\) | \(\zeta_{\varepsilon_1^{\varepsilon_1}}\) |
| \((2\uparrow\uparrow)^{2^{2^{17}+1}}3^{2^{2^{17}}}\) | \(\eta_0\) |
| \(2\uparrow\uparrow\uparrow(2\uparrow\uparrow)^23^{2^{2^{17}}}\) | \(\zeta_{\zeta_1}\) |
| \(2\uparrow\uparrow\uparrow(2\uparrow\uparrow)^{2^{2^{17}+1}}3^{2^{2^{17}}}\) | \(\zeta_{\eta_0+1}\) |
| \((2\uparrow\uparrow\uparrow)^3(2\uparrow\uparrow)^{2^{2^{17}+1}}3^{2^{2^{17}}}\) | \(\varphi_4(0)\) |