You can find the definition of Dropper Ordinal Notation (DON) here.
Up to limit of standard ordinal notation[]
| Dropper Ordinal Notation | Other OCFs |
|---|---|
| \(D[1]\) | \(\Omega\) |
| \(D[2]\) | \(\Omega_2\) |
| \(D[n]\) | \(\Omega_n\) |
| \(D[\omega]\) | \(\Omega_{\omega}\) |
| \(D[D[0]]\) | \(\Omega_{\Omega}\) |
| \(D[D[D[0]]]\) | \(\Omega_{\Omega_{\Omega}}\) |
| \(\psi_{D[D_0]}(0)\) | \(\psi_I(0)\) |
| \(\psi_{D[D_0]}(0)^{\psi_{D[D_0]}(0)}\) | \(\psi_I(0)^{\psi_I(0)}\) |
| \(\psi_{D[\psi_{D[D_0]}(0)+1]}(0)\) | \(\psi_{W\_{\psi_I(0)+1}}(0)\) |
| \(D[\psi_{D[D_0]}(0)+1]\) | \(\Omega_{\psi_I(0)+1}\) |
| \(D[\psi_{D[D_0]}(0)+D[\psi_{D[D_0]}(0)+1]]\) | \(\Omega_{\Omega_{\psi_I(0)+1}}\) |
| \(\psi_{D[D_0]}(1)\) | \(\psi_I(1)\) |
| \(\psi_{D[D_0]}(D[D_0])\) | \(\psi_I(I)\) |
| \(D[D_0]\) | \(I\) |
| \(D[D_0+1]\) | \(\Omega_{I+1}\) |
| \(D[D_0+D[D_0+1]]\) | \(\Omega_{\Omega_{I+1}}\) |
| \(D[D_02]\) | \(I_2\) |
| \(D[D_02+1]\) | \(\Omega_{I_2+1}\) |
| \(D[D_03]\) | \(I_3\) |
| \(D[D_0^2]\) | \(I(1,0)\) |
| \(D[D_0^2+1]\) | \(W_{I(1,0)+1)}\) |
| \(D[D_0^2+D_0]\) | \(I_{I(1,0)+1)}\) |
| \(D[D_0^22]\) | \(I(1,1)\) |
| \(D[D_0^3]\) | \(I(2,0)\) |
| \(D[D_0^{D_0}]\) | \(I(1,0,0)\) |
| \(D[D_1]\) | \(M\) |
| \(D[D_1+1]\) | \(\Omega_{M+1}\) |
| \(D[D_1+D_0]\) | \(I_{M+1}\) |
| \(D[D_1+D_0^2]\) | \(I(1,M+1)\) |
| \(D[D_1+D_0^{D_0}]\) | \(I(1,0,M+1)\) |
| \(D[D_1+D_0^{D_0^{\omega}}]\) | \(\chi_{M_2}(M_2^{M_2^{\omega}})\) |
| \(D[D_12]\) | \(M_2\) |
| \(D[D_1D_0]\) | \(\chi_{M(1,0)}(0)\) |
| \(D[D_1D_0+1]\) | \(W_{\chi_{M(1,0)}(0)+1}\) |
| \(D[D_1D_0+D_0]\) | \(\chi_{M(1,0)}(1)\) |
| \(D[D_1D_0+D_0^2]\) | \(\chi_{M(1,0)}(M(1,0))\) |
| \(D[D_1D_0+D_1]\) | \(M(1,0)\) |
| \(D[D_1D_0+D_12]\) | \(M_{M(1,0)+1}\) |
| \(D[D_1D_02]\) | \(\chi_{M(1,1)}(0)\) |
| \(D[D_1D_02+D_0]\) | \(M(1,1)\) |
| \(D[D_1D_03]\) | \(\chi_{M(1,1)}(0)\) |
| \(D[D_1D_0^2]\) | \(\chi_{M(2,0)}(0)\) |
| \(D[D_1D_0^{D_0}]\) | \(\chi_{M(1,0,0)}(0)\) |
| \(D[D_1^2]\) | \(\Xi[2]\) |
| \(D[D_1^2+D_0]\) | \(W_{\Xi[2]+1}\) |
| \(D[D_1^2+D_1]\) | \(M_{\Xi[2]+1}\) |
| \(D[D_1^2+D_1D_0]\) | \(\chi_{M(1,\Xi[2]+1)}(0)\) |
| \(D[D_1^22]\) | \(\Xi[2]_2\) |
| \(D[D_1^2D_0]\) | \(\chi_{\Psi_{\Xi[2](1,0)}(\Xi[2],0)}(0)\) |
| \(D[D_1^2D_0+D_1]\) | \(\Psi_{\Xi[2](1,0)}(\Xi[2],0)\) |
| \(D[D_1^2D_0+D_12]\) | \(M_{\Psi_{\Xi[2](1,0)}(\Xi[2],0)+1}\) |
| \(D[D_1^2D_0+D_1D_0+D_1]\) | \(\Psi_{\Xi[2](1,0)}(\Xi[2],1)\) |
| \(D[D_1^2D_0+D_1D_0^2]\) | \(\Psi_{\Xi[2](1,0)}(\Xi[2],\Xi[2](1,0))\) |
| \(D[D_1^2D_0+D_1^2]\) | \(\Xi[2](1,0)\) |
| \(D[D_1^2D_0+D_1^22]\) | \(\Xi[2]_{\Xi[2](1,0)+1}\) |
| \(D[D_1^2D_02+D_1^2]\) | \(\Xi[2](1,1)\) |
| \(D[D_1^2D_02+D_1^22]\) | \(\Xi[2]_{\Xi[2](1,1)+1}\) |
| \(D[D_1^2D_03+D_1^2]\) | \(\Xi[2](1,2)\) |
| \(D[D_1^2D_0^2+D_1^2]\) | \(\Xi[2](2,0)\) |
| \(D[D_1^2D_0^{D_0}+D_1^2]\) | \(\Xi[2](1,0,0)\) |
| \(D[D_1^3]\) | \(\Xi[3]\) |
| \(D[D_1^32]\) | \(\Xi[3]_2\) |
| \(D[D_1^3D_0+D_1^3]\) | \(\Xi[3](1,0)\) |
| \(D[D_1^3D_02+D_1^3]\) | \(\Xi[3](1,1)\) |
| \(D[D_1^3D_0^2+D_1^3]\) | \(\Xi[3](2,0)\) |
| \(D[D_1^4]\) | \(\Xi[4]\) |
| \(D[D_1^5]\) | \(\Xi[5]\) |
| \(D[D_1^{D_0}]\) | \(\chi_{\Xi[K](1,0)}(0)\) |
Work in progress!