无编辑摘要 标签:可视化编辑 |
无编辑摘要 标签:可视化编辑 |
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(未显示同一用户的10个中间版本) | |||
第38行: | 第38行: | ||
|2<1>2 |
|2<1>2 |
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|\(\omega2+1\) |
|\(\omega2+1\) |
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+ | |- |
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+ | |2<1>3 |
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+ | |\(\omega2+2\) |
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|- |
|- |
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|3<1>1 |
|3<1>1 |
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第77行: | 第80行: | ||
|1<2>2 |
|1<2>2 |
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|\(\omega^\omega+1\) |
|\(\omega^\omega+1\) |
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+ | |- |
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+ | |1<2>3 |
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+ | |\(\omega^\omega+2\) |
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|- |
|- |
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|1<2>1<1>1 |
|1<2>1<1>1 |
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第83行: | 第89行: | ||
|1<2>1<1>2 |
|1<2>1<1>2 |
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|\(\omega^\omega+\omega+1\) |
|\(\omega^\omega+\omega+1\) |
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+ | |- |
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+ | |1<2>1<1>3 |
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+ | |\(\omega^\omega+\omega+2\) |
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|- |
|- |
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|1<2>2<1>1 |
|1<2>2<1>1 |
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|\(\omega^\omega+\omega2\) |
|\(\omega^\omega+\omega2\) |
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+ | |- |
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+ | |1<2>3<1>1 |
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+ | |\(\omega^\omega+\omega3\) |
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|- |
|- |
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|1<2>1<1>1<1>1 |
|1<2>1<1>1<1>1 |
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第95行: | 第107行: | ||
|2<2>1 |
|2<2>1 |
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|\(\omega^\omega2\) |
|\(\omega^\omega2\) |
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+ | |- |
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+ | |3<2>1 |
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+ | |\(\omega^\omega3\) |
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|- |
|- |
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|1<1>1<2>1 |
|1<1>1<2>1 |
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|\(\omega^{\omega+1}\) |
|\(\omega^{\omega+1}\) |
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+ | |- |
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+ | |1<1>1<2>2 |
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+ | |\(\omega^{\omega+1}+1\) |
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+ | |- |
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+ | |1<1>1<2>3 |
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+ | |\(\omega^{\omega+1}+2\) |
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+ | |- |
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+ | |1<1>1<2>1<1>1 |
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+ | |\(\omega^{\omega+1}+\omega\) |
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+ | |- |
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+ | |1<1>1<2>1<1>2 |
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+ | |\(\omega^{\omega+1}+\omega+1\) |
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+ | |- |
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+ | |1<1>1<2>1<1>3 |
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+ | |\(\omega^{\omega+1}+\omega+2\) |
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+ | |- |
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+ | |1<1>1<2>2<1>1 |
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+ | |\(\omega^{\omega+1}+\omega2\) |
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+ | |- |
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+ | |1<1>1<2>3<1>1 |
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+ | |\(\omega^{\omega+1}+\omega3\) |
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+ | |- |
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+ | |1<1>1<2>1<1>1<1>1 |
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+ | |\(\omega^{\omega+1}+\omega^2\) |
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+ | |- |
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+ | |1<1>1<2>1<1>1<1>1<1>1 |
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+ | |\(\omega^{\omega+1}+\omega^3\) |
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|- |
|- |
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|1<1>2<2>1 |
|1<1>2<2>1 |
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|\(\omega^{\omega+1}+\omega^\omega\) |
|\(\omega^{\omega+1}+\omega^\omega\) |
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+ | |- |
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+ | |1<1>3<2>1 |
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+ | |\(\omega^{\omega+1}+\omega^\omega2\) |
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|- |
|- |
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|2<1>1<2>1 |
|2<1>1<2>1 |
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第122行: | 第167行: | ||
|1<1<1>1>1 |
|1<1<1>1>1 |
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|\(\omega^{\omega^\omega}\) |
|\(\omega^{\omega^\omega}\) |
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+ | |- |
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+ | |2<1<1>1>1 |
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+ | |\(\omega^{\omega^\omega}2\) |
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+ | |- |
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+ | |1<1<1>1>1<1<1>1>1 |
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+ | |\(\omega^{\omega^\omega2}\) |
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+ | |- |
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+ | |1<1<1>1>1<1<1>1>1<1<1>1>1 |
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+ | |\(\omega^{\omega^\omega3}\) |
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|- |
|- |
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|1<1<1>2>1 |
|1<1<1>2>1 |
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第153行: | 第207行: | ||
|1<1/1>2 |
|1<1/1>2 |
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|\(\varepsilon_0+1\) |
|\(\varepsilon_0+1\) |
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+ | |- |
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+ | |1<1/1>3 |
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+ | |\(\varepsilon_0+2\) |
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|- |
|- |
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|1<1/1>1<1>1 |
|1<1/1>1<1>1 |
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|\(\varepsilon_0+\omega\) |
|\(\varepsilon_0+\omega\) |
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+ | |- |
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+ | |1<1/1>1<1>2 |
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+ | |\(\varepsilon_0+\omega+1\) |
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+ | |- |
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+ | |1<1/1>1<1>3 |
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+ | |\(\varepsilon_0+\omega+2\) |
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+ | |- |
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+ | |1<1/1>2<1>1 |
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+ | |\(\varepsilon_0+\omega2\) |
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+ | |- |
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+ | |1<1/1>3<1>1 |
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+ | |\(\varepsilon_0+\omega3\) |
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+ | |- |
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+ | |1<1/1>1<1>1<1>1 |
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+ | |\(\varepsilon_0+\omega^2\) |
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+ | |- |
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+ | |1<1/1>1<1>1<1>1<1>1 |
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+ | |\(\varepsilon_0+\omega^3\) |
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+ | |- |
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+ | |1<1/1>1<2>1 |
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+ | |\(\varepsilon_0+\omega^\omega\) |
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|- |
|- |
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|1<1/1>1<1<1/1>1>1 |
|1<1/1>1<1<1/1>1>1 |
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第219行: | 第297行: | ||
|1<2/1>1 |
|1<2/1>1 |
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|\(BHO\) |
|\(BHO\) |
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+ | |- |
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+ | |1<2/1>1<1<2/1>1>1 |
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+ | |\(\psi(\psi_1(0))2\) |
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+ | |- |
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+ | |1<2/1>1<1<2/1>2>1 |
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+ | |\(\psi(\psi_1(0))^\omega\) |
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+ | |- |
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+ | |1<2/1>1<1<2/1>1<1<2/1>1>1>1 |
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+ | |\(\psi(\psi_1(0))^{\psi(\psi_1(0))}\) |
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+ | |- |
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+ | |1<2/1>1<1/1>1 |
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+ | |\(\psi(\psi_1(0)+1)\) |
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+ | |- |
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+ | |1<2/1>1<1/1>1<1/1>1 |
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+ | |\(\psi(\psi_1(0)+\Omega)\) |
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+ | |- |
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+ | |1<2/1>1<1/2>1 |
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+ | |\(\psi(\psi_1(0)+\Omega^\omega)\) |
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+ | |- |
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+ | |1<2/1>1<1/1<2/1>1>1 |
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+ | |\(\psi(\psi_1(0)2)\) |
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+ | |- |
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+ | |1<2/1>1<1/1<2/1>2>1 |
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+ | |\(\psi(\psi_1(0)^\omega)\) |
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+ | |- |
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+ | |1<2/1>1<1/1<2/1>1<1<2/1>1>1>1 |
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+ | |\(\psi(\psi_1(0)^{\psi(\psi_1(0))})\) |
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+ | |- |
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+ | |1<2/1>1<1/1<2/1>1<1/1>1>1 |
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+ | |\(\psi(\psi_1(0)^\Omega)\) |
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+ | |- |
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+ | |1<2/1>1<1/1<2/1>1<1/1<2/1>1>1>1 |
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+ | |\(\psi(\psi_1(0)^{\psi_1(0)})\) |
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+ | |- |
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+ | |2<2/1>1 |
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+ | |\(\psi(\psi_1(1))\) |
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+ | |- |
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+ | |3<2/1>1 |
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+ | |\(\psi(\psi_1(2))\) |
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+ | |- |
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+ | |1<1<2/1>1>1<2/1>1 |
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+ | |\(\psi(\psi_1(\psi(\psi_1(0))))\) |
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+ | |- |
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+ | |1<1/1>1<2/1>1 |
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+ | |\(\psi(\psi_1(\Omega))\) |
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+ | |- |
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+ | |1<1/1<2/1>1>1<2/1>1 |
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+ | |\(\psi(\psi_1(\psi_1(0)))\) |
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+ | |- |
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+ | |1<1/1<1/1<2/1>1>1<2/1>1>1<2/1>1 |
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+ | |\(\psi(\psi_1(\psi_1(\psi_1(0))))\) |
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|- |
|- |
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|1<2/1>1<2/1>1 |
|1<2/1>1<2/1>1 |
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|\(\psi(\Omega_2)\) |
|\(\psi(\Omega_2)\) |
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+ | |- |
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+ | |1<2/2>1 |
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+ | |\(\psi(\Omega_2^\omega)\) |
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+ | |- |
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+ | |1<2/1<1/1>1>1 |
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+ | |\(\psi(\Omega_2^\Omega)\) |
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+ | |- |
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+ | |1<2/1<2/1>1>1 |
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+ | |\(\psi(\Omega_2^{\Omega_2})\) |
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+ | |- |
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+ | |1<2/1<2/1<2/1>1>1>1 |
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+ | |<nowiki>\(\psi(\Omega_2^{\Omega_2^{\Omega_2}})\)</nowiki> |
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|- |
|- |
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|1<3/1>1 |
|1<3/1>1 |
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第256行: | 第397行: | ||
这里特别注意:1<1/1>2=1<1<1/1>1>2,而2<1/1>1=1<2<1/1>1>1,其中2所在的位置并不相同! |
这里特别注意:1<1/1>2=1<1<1/1>1>2,而2<1/1>1=1<2<1/1>1>1,其中2所在的位置并不相同! |
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+ | |||
+ | <br /> |
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{| class="fandom-table" |
{| class="fandom-table" |
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+ | |+反射模式分析 |
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− | |+MOTAN增长率分析(\(\psi(\psi_I(0))\)以上) |
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+ | |1<1>1 |
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− | !MOTAN |
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+ | |1 |
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− | !FGH |
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|- |
|- |
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− | | |
+ | |1<1>1<1>1 |
+ | |1-1 |
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− | |\(\psi(\psi_I(1))\) |
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|- |
|- |
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− | |1< |
+ | |1<1>1<1>1<1>1 |
+ | |1-1-1 |
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− | |\(\psi(\psi_I(\psi_I(0)))\) |
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|- |
|- |
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− | |1< |
+ | |1<1/1>1 |
+ | |2 |
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− | |\(\psi(I)\) |
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|- |
|- |
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− | |1<1 |
+ | |1<1<1>1/1>1 |
+ | |1-2 |
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− | |\(\psi(I^\omega)\) |
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|- |
|- |
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− | |1<1/ |
+ | |1<1/1/1>1 |
+ | |2 1-2 |
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− | |\(\psi(\psi_{I+1}(0))\) |
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− | |- |
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− | |1<2/1/1>1 |
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− | |\(\psi(\psi_{I_2}(0))\) |
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|- |
|- |
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|1<1/1/1/1>1 |
|1<1/1/1/1>1 |
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+ | |2 1-(2 1-2) |
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− | |\(\psi(\psi_{I(1,0)}(0))\) |
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− | |- |
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− | |1<1{2}1>1 |
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− | |\(\psi(\psi_{I(\omega,0)}(0))\) |
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|- |
|- |
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|1<1{1{1}1}1>1 |
|1<1{1{1}1}1>1 |
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+ | |2-2 |
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− | |\(\psi(\psi_{I(1,0,0)}(0))\)=\(\psi(\psi_{\chi(M)}(0))\) |
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− | |- |
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− | |2<1{1{1}1}1>1 |
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− | |\(\psi(M)\)=\(\psi(\psi_{I(2,0,0)}(0))\) |
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− | |- |
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− | |1<1{1{1}1}1>1<1{1{1}1}1>1 |
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− | |\(\psi(M^2)\)=\(\psi(\psi_{I(1,0,0,0)}(0))\) |
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− | |- |
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− | |1<1{1{1}1}2>1 |
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− | |\(\psi(M^\omega)\) |
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− | |- |
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− | |1<1{1{1}1}1<1{1<1{1{1}1}1>1}1>1>1 |
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− | |\(\psi(M^\chi(M))\) |
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− | |- |
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− | |1<1{1{1}1}1<1{1{1}1}1>1>1 |
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− | |\(\psi(M^M)\) |
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− | |- |
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− | |1<1{1{1}1}1{1}1>1 |
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− | |\(\psi(\psi_{\chi(\Omega_{M+1})}(0))\) |
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− | |- |
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− | |1<1{1{1}1}1{1}1{1}1>1 |
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− | |\(\psi(\psi_{\chi(I_{M+1})}(0))\) |
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− | |- |
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− | |1<1{1{1}1}1{1}1{1}1{1}1>1 |
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− | |\(\psi(\psi_{\chi(I(1,M+1))}(0))\) |
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− | |- |
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− | |1<1{1{1}1}1{2}1>1 |
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− | |\(\psi(\psi_{\chi(I(\omega,M+1))}(0))\) |
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− | |- |
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− | |1<2{1{1}1}1>1 |
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− | |\(\psi(\psi_{\chi(M_2)}(0))\) |
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− | |- |
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− | |1<1<1{1{1}1}1>1{1{1}1}1>1 |
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− | |\(\psi(\psi_{\chi(M_M)}(0))\) |
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|- |
|- |
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|1<1{1}1{1{1}1}1>1 |
|1<1{1}1{1{1}1}1>1 |
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+ | |2 1-2-2 |
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− | |\(\psi(\psi_{\chi(M[(1,0)])}(0))\) |
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|- |
|- |
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− | |1<1{1} |
+ | |1<1{1}1{1}1{1{1}1}1>1 |
+ | |2 1-(2 1-2-2) |
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− | |\(\psi(\psi_{\chi(M_{M[(1,0)]+1})}(0))\) |
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|- |
|- |
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− | |1< |
+ | |1<1{1{1}1}1{1{1}1}1>1 |
+ | |2-2 1-2-2 |
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− | |\(\psi(\psi_{\chi(M[(1,1)])}(0))\) |
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|- |
|- |
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− | |1<1{ |
+ | |1<1{2{1}1}1>1 |
+ | |2-2-2 |
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− | |\(\psi(\psi_{\chi(M[(2,0)])}(0))\) |
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|- |
|- |
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− | |1<1{ |
+ | |1<1{3{1}1}1>1 |
+ | |2-2-2-2 |
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− | |\(\psi(\psi_{\chi(M[(\omega,0)])}(0))\) |
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|- |
|- |
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− | |1<1{1{ |
+ | |1<1{1{1}1{1}1}1>1 |
+ | |3 |
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− | |\(\psi(\psi_{\chi(M[1,0])}(0))\) |
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|- |
|- |
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− | |1< |
+ | |1<1{1}1{1{1}1{1}1}1>1 |
+ | |2 1-3 |
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− | |\(\psi(\psi_{\chi(M[2,0])}(0))\) |
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|- |
|- |
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− | |1<1{1{1} |
+ | |1<1{1}1{1}1{1{1}1{1}1}1>1 |
+ | |2 1-(2 1-3) |
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− | |\(\psi(\psi_{\chi(M[\omega,0])}(0))\) |
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|- |
|- |
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− | |1<1{ |
+ | |1<1{1{1}1}1{1{1}1{1}1}1>1 |
+ | |2-2 1-3 |
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− | |\(\psi(\psi_{\chi(M[1,0,0])}(0))\)=\(\psi(\psi_{\chi(N)}(0))\) |
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− | |} |
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− | <br /> |
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− | {| class="fandom-table" |
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− | |+MOTAN表达式对应的反射序数 |
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− | !MOTAN |
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− | !反射序数 |
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|- |
|- |
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+ | |1<1{1}1{1{1}1}1{1{1}1{1}1}1>1 |
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− | |1<1>1 |
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+ | |2 1-(2-2 1-3) |
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− | |\(\Pi_1 反射\) |
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|- |
|- |
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− | |1<1 |
+ | |1<1{1{1}1}1{1{1}1}1{1{1}1{1}1}1>1 |
+ | |2-2 1-(2-2 1-3) |
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− | |\(\Pi_1 反射 onto \Pi_1 反射\) |
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|- |
|- |
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− | |1<1 |
+ | |1<1{2{1}1}1{1{1}1{1}1}1>1 |
+ | |2-2-2 1-3 |
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− | |\(\Pi_2 反射\) |
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|- |
|- |
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− | |1<1 |
+ | |1<1{1{1}1{1}1}1{1{1}1{1}1}1>1 |
+ | |3 1-3 |
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− | |\(\Pi_1 反射 onto \Pi_2 反射\) |
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|- |
|- |
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+ | |1<1{1{1}1{1}1}1{1{1}1{1}1}1{1{1}1{1}1}1>1 |
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− | |1<1/1/1>1 |
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+ | |3 1-(3 1-3) |
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− | |\(\Pi_2 反射 且 \Pi_1 反射 onto \Pi_2 反射\) |
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|- |
|- |
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− | |1<1 |
+ | |1<1{1{1}2{1}1}1>1 |
+ | |2-3 |
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− | |\(\Pi_1 反射 onto (\Pi_2 反射 且 \Pi_1 反射 onto \Pi_2 反射)\) |
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|- |
|- |
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− | |1<1 |
+ | |1<1{1{1}3{1}1}1>1 |
+ | |2-2-3 |
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− | |\(\Pi_2 反射 且 \Pi_1 反射 onto (\Pi_2 反射 且 \Pi_1 反射 onto \Pi_2 反射)\) |
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|- |
|- |
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− | |1<1{1{1}1}1>1 |
+ | |1<1{2{1}1{1}1}1>1 |
+ | |3 2-3 |
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− | |\(\Pi_2 反射 onto \Pi_2 反射\) |
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|- |
|- |
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− | |1<1{ |
+ | |1<1{3{1}1{1}1}1>1 |
+ | |3 2-(3 2-3) |
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− | |\(\Pi_2 反射 onto \Pi_2 反射 onto \Pi_2 反射\) |
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|- |
|- |
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− | |1<1{1{1}1{1}1}1>1 |
+ | |1<1{1{1}1{1}1{1}1}1>1 |
+ | |3-3 |
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− | |\(\Pi_3 反射\) |
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|- |
|- |
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− | |1<1{1{1}1{1}1{1}1}1>1 |
+ | |1<1{1{1}1{1}1{1}1{1}1}1>1 |
+ | |3-3-3 |
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− | |\(\Pi_3 反射 onto \Pi_3 反射\) |
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|- |
|- |
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|1<1{1{1{1}1}1}1>1 |
|1<1{1{1{1}1}1}1>1 |
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+ | |4 |
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− | |\(\Pi_4 反射\) |
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|} |
|} |
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[[Category:博客帖子]] |
[[Category:博客帖子]] |
2021年11月5日 (五) 02:37的最新版本
当n为自然数时,MOTAN的b[n]p跟BEAF的b{n}p是完全相同的,b[n]p=b\(\uparrow^n\)p
3[1<1>2]2=3[1<1>1]3=3[3]3
3[1<1>2]3=3[1<1>1]3[1<1>1]3=3[1<1>1](3[3]3)=3[3[3]3](3[3]3)>3[3[3]3]3>3[4]3=3\(\uparrow\uparrow\uparrow\uparrow\)3=G(1)
3[1<1>2]4>3[1<1>1](G(1))>3[G(1)]3=G(2)
......
3[1<1>2]66>G(64)
MOTAN | FGH |
---|---|
1 | \(2\) |
2 | \(3\) |
3 | \(4\) |
1<1>1 | \(\omega\) |
1<1>2 | \(\omega+1\) |
1<1>3 | \(\omega+2\) |
2<1>1 | \(\omega2\) |
2<1>2 | \(\omega2+1\) |
2<1>3 | \(\omega2+2\) |
3<1>1 | \(\omega3\) |
1<1>1<1>1 | \(\omega^2\) |
1<1>1<1>2 | \(\omega^2+1\) |
1<1>1<1>3 | \(\omega^2+2\) |
1<1>2<1>1 | \(\omega^2+\omega\) |
1<1>2<1>2 | \(\omega^2+\omega+1\) |
1<1>2<1>3 | \(\omega^2+\omega+2\) |
1<1>3<1>1 | \(\omega^2+\omega2\) |
2<1>1<1>1 | \(\omega^22\) |
3<1>1<1>1 | \(\omega^23\) |
1<1>1<1>1<1>1 | \(\omega^3\) |
1<2>1 | \(\omega^\omega\) |
1<2>2 | \(\omega^\omega+1\) |
1<2>3 | \(\omega^\omega+2\) |
1<2>1<1>1 | \(\omega^\omega+\omega\) |
1<2>1<1>2 | \(\omega^\omega+\omega+1\) |
1<2>1<1>3 | \(\omega^\omega+\omega+2\) |
1<2>2<1>1 | \(\omega^\omega+\omega2\) |
1<2>3<1>1 | \(\omega^\omega+\omega3\) |
1<2>1<1>1<1>1 | \(\omega^\omega+\omega^2\) |
1<2>1<1>1<1>1<1>1 | \(\omega^\omega+\omega^3\) |
2<2>1 | \(\omega^\omega2\) |
3<2>1 | \(\omega^\omega3\) |
1<1>1<2>1 | \(\omega^{\omega+1}\) |
1<1>1<2>2 | \(\omega^{\omega+1}+1\) |
1<1>1<2>3 | \(\omega^{\omega+1}+2\) |
1<1>1<2>1<1>1 | \(\omega^{\omega+1}+\omega\) |
1<1>1<2>1<1>2 | \(\omega^{\omega+1}+\omega+1\) |
1<1>1<2>1<1>3 | \(\omega^{\omega+1}+\omega+2\) |
1<1>1<2>2<1>1 | \(\omega^{\omega+1}+\omega2\) |
1<1>1<2>3<1>1 | \(\omega^{\omega+1}+\omega3\) |
1<1>1<2>1<1>1<1>1 | \(\omega^{\omega+1}+\omega^2\) |
1<1>1<2>1<1>1<1>1<1>1 | \(\omega^{\omega+1}+\omega^3\) |
1<1>2<2>1 | \(\omega^{\omega+1}+\omega^\omega\) |
1<1>3<2>1 | \(\omega^{\omega+1}+\omega^\omega2\) |
2<1>1<2>1 | \(\omega^{\omega+1}2\) |
1<1>1<1>1<2>1 | \(\omega^{\omega+2}\) |
1<1>1<1>1<1>1<2>1 | \(\omega^{\omega+3}\) |
1<2>1<2>1 | \(\omega^{\omega2}\) |
1<2>1<2>1<2>1 | \(\omega^{\omega3}\) |
1<3>1 | \(\omega^{\omega^2}\) |
1<1<1>1>1 | \(\omega^{\omega^\omega}\) |
2<1<1>1>1 | \(\omega^{\omega^\omega}2\) |
1<1<1>1>1<1<1>1>1 | \(\omega^{\omega^\omega2}\) |
1<1<1>1>1<1<1>1>1<1<1>1>1 | \(\omega^{\omega^\omega3}\) |
1<1<1>2>1 | \(\omega^{\omega^{\omega+1}}\) |
1<2<1>1>1 | \(\omega^{\omega^{\omega2}}\) |
1<1<1>1<1>1>1 | \(\omega^{\omega^{\omega^2}}\) |
1<1<1>1<1>1<1>1>1 | \(\omega^{\omega^{\omega^3}}\) |
1<1<2>1>1 | \(\omega^{\omega^{\omega^\omega}}\) |
1<1<1<1>1>1>1 | \(\omega^{\omega^{\omega^{\omega^\omega}}}\) |
1<1/1>1 | \(\varepsilon_0\) |
MOTAN | FGH |
---|---|
1<1/1>2 | \(\varepsilon_0+1\) |
1<1/1>3 | \(\varepsilon_0+2\) |
1<1/1>1<1>1 | \(\varepsilon_0+\omega\) |
1<1/1>1<1>2 | \(\varepsilon_0+\omega+1\) |
1<1/1>1<1>3 | \(\varepsilon_0+\omega+2\) |
1<1/1>2<1>1 | \(\varepsilon_0+\omega2\) |
1<1/1>3<1>1 | \(\varepsilon_0+\omega3\) |
1<1/1>1<1>1<1>1 | \(\varepsilon_0+\omega^2\) |
1<1/1>1<1>1<1>1<1>1 | \(\varepsilon_0+\omega^3\) |
1<1/1>1<2>1 | \(\varepsilon_0+\omega^\omega\) |
1<1/1>1<1<1/1>1>1 | \(\varepsilon_02\) |
1<1/1>2<1<1/1>1>1 | \(\varepsilon_03\) |
1<1/1>1<1<1/1>1>1<1<1/1>1>1 | \(\varepsilon_0^2\) |
1<1/1>1<1<1/1>2>1 | \(\varepsilon_0^\omega\) |
1<1/1>1<1<1/1>1<1<1/1>1>1>1 | \(\varepsilon_0^{\varepsilon_0}\) |
1<1/1>1<1<1/1>1<1<1/1>1<1<1/1>1>1>1>1 | \(\varepsilon_0^{\varepsilon_0^{\varepsilon_0}}\) |
2<1/1>1 | \(\varepsilon_1\) |
3<1/1>1 | \(\varepsilon_2\) |
1<1>1<1/1>1 | \(\varepsilon_{\omega}\) |
1<1<1/1>1>1<1/1>1 | \(\varepsilon_{\varepsilon_0}\) |
1<1<1<1/1>1>1<1/1>1>1<1/1>1 | \(\varepsilon_{\varepsilon_{\varepsilon_0}}\) |
1<1/1>1<1/1>1 | \(\zeta_0\) |
1<1/1>2<1/1>1 | \(\varepsilon_{\zeta_0+1}\) |
2<1/1>1<1/1>1 | \(\zeta_1\) |
1<1/1>1<1/1>1<1/1>1 | \(\eta_0\) |
1<1/2>1 | \(\varphi(\omega,0)\) |
1<1/1<1<1/1>1>1>1 | \(\varphi(\varphi(\omega,0),0)\) |
1<1/1<1/1>1>1 | \(\Gamma_0\) |
1<1/1<1>1<1/1>1>1 | \(SVO\) |
1<1/1<1/1>1<1/1>1>1 | \(LVO\) |
1<2/1>1 | \(BHO\) |
1<2/1>1<1<2/1>1>1 | \(\psi(\psi_1(0))2\) |
1<2/1>1<1<2/1>2>1 | \(\psi(\psi_1(0))^\omega\) |
1<2/1>1<1<2/1>1<1<2/1>1>1>1 | \(\psi(\psi_1(0))^{\psi(\psi_1(0))}\) |
1<2/1>1<1/1>1 | \(\psi(\psi_1(0)+1)\) |
1<2/1>1<1/1>1<1/1>1 | \(\psi(\psi_1(0)+\Omega)\) |
1<2/1>1<1/2>1 | \(\psi(\psi_1(0)+\Omega^\omega)\) |
1<2/1>1<1/1<2/1>1>1 | \(\psi(\psi_1(0)2)\) |
1<2/1>1<1/1<2/1>2>1 | \(\psi(\psi_1(0)^\omega)\) |
1<2/1>1<1/1<2/1>1<1<2/1>1>1>1 | \(\psi(\psi_1(0)^{\psi(\psi_1(0))})\) |
1<2/1>1<1/1<2/1>1<1/1>1>1 | \(\psi(\psi_1(0)^\Omega)\) |
1<2/1>1<1/1<2/1>1<1/1<2/1>1>1>1 | \(\psi(\psi_1(0)^{\psi_1(0)})\) |
2<2/1>1 | \(\psi(\psi_1(1))\) |
3<2/1>1 | \(\psi(\psi_1(2))\) |
1<1<2/1>1>1<2/1>1 | \(\psi(\psi_1(\psi(\psi_1(0))))\) |
1<1/1>1<2/1>1 | \(\psi(\psi_1(\Omega))\) |
1<1/1<2/1>1>1<2/1>1 | \(\psi(\psi_1(\psi_1(0)))\) |
1<1/1<1/1<2/1>1>1<2/1>1>1<2/1>1 | \(\psi(\psi_1(\psi_1(\psi_1(0))))\) |
1<2/1>1<2/1>1 | \(\psi(\Omega_2)\) |
1<2/2>1 | \(\psi(\Omega_2^\omega)\) |
1<2/1<1/1>1>1 | \(\psi(\Omega_2^\Omega)\) |
1<2/1<2/1>1>1 | \(\psi(\Omega_2^{\Omega_2})\) |
1<2/1<2/1<2/1>1>1>1 | \(\psi(\Omega_2^{\Omega_2^{\Omega_2}})\) |
1<3/1>1 | \(\psi(\psi_2(0))\) |
1<3/1>1<3/1>1 | \(\psi(\Omega_3)\) |
1<1<1>1/1>1 | \(\psi(\Omega_{\omega})\) |
1<1<1>2/1>1 | \(\psi(\psi_{\omega}(0))\) |
1<1<1/1>1/1>1 | \(\psi(\Omega_{\Omega})\) |
1<1<1<1/1>1/1>1/1>1 | \(\psi(\Omega_{\Omega_{\Omega}})\) |
1<1/1/1>1 | \(\psi(\psi_I(0))\) |
1<1/1>1是1<1<1/1>1>1的省略写法,省略了最外层的1<>1,它们都是\(\varepsilon_0\)。
1<1/1>2跟1<1<1/1>1>2表示同一序数,都是\(\varepsilon_0+1\)。
1<1/1>1<1<1/1>1>1和2<1<1/1>1>1表示同一序数,都是\(\varepsilon_02\)。
1<1/1>1<1>1<1<1/1>1>1和1<1>1<1<1/1>1>1表示同一序数,都是\(\varepsilon_0\omega\),此时第1个式子开头的1<1/1>1变成了并不影响表达式增长率的“前缀”。
1<1<1/1>2>1和1<1/1>1<1<1/1>2>1表示的都是\(\varepsilon_0^\omega\)
2<1/1>1和1<2<1/1>1>1表示的是同一序数,都是\(\varepsilon_1\)。
这里特别注意:1<1/1>2=1<1<1/1>1>2,而2<1/1>1=1<2<1/1>1>1,其中2所在的位置并不相同!
1<1>1 | 1 |
1<1>1<1>1 | 1-1 |
1<1>1<1>1<1>1 | 1-1-1 |
1<1/1>1 | 2 |
1<1<1>1/1>1 | 1-2 |
1<1/1/1>1 | 2 1-2 |
1<1/1/1/1>1 | 2 1-(2 1-2) |
1<1{1{1}1}1>1 | 2-2 |
1<1{1}1{1{1}1}1>1 | 2 1-2-2 |
1<1{1}1{1}1{1{1}1}1>1 | 2 1-(2 1-2-2) |
1<1{1{1}1}1{1{1}1}1>1 | 2-2 1-2-2 |
1<1{2{1}1}1>1 | 2-2-2 |
1<1{3{1}1}1>1 | 2-2-2-2 |
1<1{1{1}1{1}1}1>1 | 3 |
1<1{1}1{1{1}1{1}1}1>1 | 2 1-3 |
1<1{1}1{1}1{1{1}1{1}1}1>1 | 2 1-(2 1-3) |
1<1{1{1}1}1{1{1}1{1}1}1>1 | 2-2 1-3 |
1<1{1}1{1{1}1}1{1{1}1{1}1}1>1 | 2 1-(2-2 1-3) |
1<1{1{1}1}1{1{1}1}1{1{1}1{1}1}1>1 | 2-2 1-(2-2 1-3) |
1<1{2{1}1}1{1{1}1{1}1}1>1 | 2-2-2 1-3 |
1<1{1{1}1{1}1}1{1{1}1{1}1}1>1 | 3 1-3 |
1<1{1{1}1{1}1}1{1{1}1{1}1}1{1{1}1{1}1}1>1 | 3 1-(3 1-3) |
1<1{1{1}2{1}1}1>1 | 2-3 |
1<1{1{1}3{1}1}1>1 | 2-2-3 |
1<1{2{1}1{1}1}1>1 | 3 2-3 |
1<1{3{1}1{1}1}1>1 | 3 2-(3 2-3) |
1<1{1{1}1{1}1{1}1}1>1 | 3-3 |
1<1{1{1}1{1}1{1}1{1}1}1>1 | 3-3-3 |
1<1{1{1{1}1}1}1>1 | 4 |