FANDOM


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!

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