大數學 维基:沙盒

這裡可以給您測試一些代碼，但如果是跟大數有關的百科條目，建議直接去創建新條目。（請不要將這行刪除，也請在橫線下面測試）

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\(這是代碼。1234567890 \space 10^{100 \uparrow 100}\)

\(\color{red}{123}\) \(\color{cyan}{\psi}\)

\(\large googol\) googol

\(\mathbb{ABCdef789}\)

\(f_{\alpha}= n= 10^{100}\underbrace{\uparrow\ldots\uparrow}_{10^{100}}10^{100},f_\Sigma(f_\zeta(f_\gamma(f_\lambda(F^{\Pi^(f_\Sigma(f_\zeta(f_\gamma(f_\lambda({\text{CA}_{n+3^{n+3^{n+3^{.^{.^{.^{n+3^{1+3}}}}}}} \rightarrow n+3^{n+3^{n+3^{.^{.^{.^{n+3^{2+3}}}}}}} \rightarrow n+3^{n+3^{n+3^{.^{.^{.^{n+3^{3+3}}}}}}} \cdots\cdots \rightarrow n+3^{n+3^{n+3^{.^{.^{.^{n+3^{n+3}}}}}}}+n+{\text{CA}^{\text{BI}^{n+{\text{CA}^{\text{BI}^{n+{\text{CA}^{\text{BI}^{.^{.^{.^{n+{\text{CA} ^{\text{BI}}}}}}}}}}}}}}}}}_ (f_\Sigma(f_\zeta(f_\gamma(f_\lambda({\text{CA}_{n+3^{n+3^{n+3^{.^{.^{.^{n+3^{1+3}}}}}}} \rightarrow n+3^{n+3^{n+3^{.^{.^{.^{n+3^{2+3}}}}}}} \rightarrow n+3^{n+3^{n+3^{.^{.^{.^{n+3^{3+3}}}}}}} \cdots\cdots \rightarrow n+3^{n+3^{n+3^{.^{.^{.^{n+3^{n+3}}}}}}}+n+{\text{CA} ^{\text{BI}^{n+{\text{CA}^{\text{BI}^{n+{\text{CA}^{\text{BI}^{.^{.^{.^{n+{\text{CA}^{\text{BI}}}}}}}}}}}}}}}}}}_ (f_\Sigma(f_\zeta(f_\gamma(f_\lambda(f^{\Pi^{\text{CA}_{n+3^{n+3^{n+3^{.^{.^{.^{n+3^{1+3}}}}}}} \rightarrow n+3^{n+3^{n+3^{.^{.^{.^{n+3^{2+3}}}}}}} \rightarrow n+3^{n+3^{n+3^{.^{.^{.^{n+3^{3+3}}}}}}} \cdots\cdots \rightarrow n+3^{n+3^{n+3^{.^{.^{.^{n+3^{n+3}}}}}}}+n+{\text{CA}^{\text{BI}^{n+{\text{CA}^{\text{BI}^{n+{\text{CA}^{\text{BI}^{.^{.^{.^{n+{\text{CA} ^{\text{BI}}}}}}}}}}}}}}}}}_{\text{CA}_{n+3^{n+3^{n+3^{.^{.^{.^{n+3^{1+3}}}}}}} \rightarrow n+3^{n+3^{n+3^{.^{.^{.^{n+3^{2+3}}}}}}} \rightarrow n+3^{n+3^{n+3^{.^{.^{.^{n+3^{3+3}}}}}}} \cdots\cdots \rightarrow n+3^{n+3^{n+3^{.^{.^{.^{n+3^{n+3}}}}}}}+n+{\text{CA} ^{\text{BI}^{n+{\text{CA}^{\text{BI}^{n+{\text{CA}^{\text{BI}^{.^{.^{.^{n+{\text{CA}^{\text{BI}}}}}}}}}}}}}}}}}}_{\omega_{\theta_{\Psi_{\text{CA}_{\vartheta_{\omega^{\epsilon_{\zeta_{\eta_{\Gamma_{\psi_{\chi_{\Phi_{\({\underbrace{\Omega_{\Omega_{\Omega_{._{._{._{\Omega}}}}}}}_{F_{7}{\Omega’s}}}\)_{\({\underbrace{I({I({I({\cdots({I({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{I’s}}}\)_{\({\underbrace{M({M({M({\cdots({M({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{M’s}}}\)_{\({\underbrace{K({K({K({\cdots({K({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{K’s}}}\)}}}}}}}}}text{CA} _{\theta_{\Psi_{\vartheta_{\omega^{\chi_{\Phi_{\({\underbrace{\Omega_{\Omega_{\Omega_{._{._{._{\Omega}}}}}}}_{F_{7}{\Omega’s}}}\)_{\({\underbrace{I({I({I({\cdots({I({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{I’s}}}\)_{\({\underbrace{M({M({M({\cdots({M({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{M’s}}}\)_{\({\underbrace{K({K({K({\cdots({K({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{K’s}}}\)}}}}}}}}}})}(\theta_{\Psi_{\text{CA}_{\Psi_{\chi_{\Phi_{ {\vartheta_{\omega^{\epsilon_{\zeta_{\eta_{\Gamma_{\({\underbrace{\Omega_{\Omega_{\Omega_{._{._{._{\Omega}}}}}}}_{F_{7}{\Omega’s}}}\)_{\({\underbrace{I({I({I({\cdots({I({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{I’s}}}\)_{\({\underbrace{M({M({M({\cdots({M({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{M’s}}}\)_{\({\underbrace{K({K({K({\cdots({K({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{K’s}}}\)}}}}}}}}}}}}}}})(\text{CA} _{\theta_{\vartheta_{\omega^{\chi_{\Phi_{\Omega_{\Omega_{\Omega_{._{._{._{\Omega_{\({\underbrace{I({I({I({\cdots({I({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{I’s}}}\)_{\({\underbrace{M({M({M({\cdots({M({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{M’s}}}\)_{\({\underbrace{K({K({K({\cdots({K({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{K’s}}}\)}}}}}}}}}}}}}}}})}}}}}}+1 \rightarrow {\text{CA} _{\theta_{\Psi_{\vartheta_{\omega^{\epsilon_{\zeta_{\eta_{\Gamma_{\psi_{\chi_{\Phi_{\({\underbrace{\Omega_{\Omega_{\Omega_{._{._{._{\Omega}}}}}}}_{F_{7}{\Omega’s}}}\)_{\({\underbrace{I({I({I({\cdots({I({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{I’s}}}\)_{\({\underbrace{M({M({M({\cdots({M({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{M’s}}}\)_{\({\underbrace{K({K({K({\cdots({K({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{K’s}}}\)}}}}}}}}}(\theta_{\Psi_{\text{CA}_{\vartheta_{\omega^{\chi_{\Phi_{\({\underbrace{\Omega_{\Omega_{\Omega_{._{._{._{\Omega}}}}}}}_{F_{7}{\Omega’s}}}\)_{\({\underbrace{I({I({I({\cdots({I({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{I’s}}}\)_{\({\underbrace{M({M({M({\cdots({M({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{M’s}}}\)_{\({\underbrace{K({K({K({\cdots({K({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{K’s}}}\)}}}}}}}}}})}(\theta_{\Psi_{\text{CA}_{\chi_{\Phi_{ {\vartheta_{\omega^{\epsilon_{\zeta_{\eta_{\Gamma_{\({\underbrace{\Omega_{\Omega_{\Omega_{._{._{._{\Omega}}}}}}}_{F_{7}{\Omega’s}}}\)_{\({\underbrace{I({I({I({\cdots({I({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{I’s}}}\)_{\({\underbrace{M({M({M({\cdots({M({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{M’s}}}\)_{\({\underbrace{K({K({K({\cdots({K({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{K’s}}}\)}}}}}}}}}}}}}})(\theta_{\Psi_{\text{CA}_{\vartheta_{\omega^{\chi_{\Phi_{\Omega_{\Omega_{\Omega_{._{._{._{\Omega_{\({\underbrace{I({I({I({\cdots({I({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{I’s}}}\)_{\({\underbrace{M({M({M({\cdots({M({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{M’s}}}\)_{\({\underbrace{K({K({K({\cdots({K({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{K’s}}}\)}}}}}}}}}}}}}}}}})}}}}}}+1 \rightarrow {\text{CA} _{\theta_{\Psi_{\vartheta_{\omega^{\epsilon_{\zeta_{\eta_{\Gamma_{\psi_{\chi_{\Phi_{\({\underbrace{\Omega_{\Omega_{\Omega_{._{._{._{\Omega}}}}}}}_{F_{7}{\Omega’s}}}\)_{\({\underbrace{I({I({I({\cdots({I({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{I’s}}}\)_{\({\underbrace{M({M({M({\cdots({M({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{M’s}}}\)_{\({\underbrace{K({K({K({\cdots({K({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{K’s}}}\)}}}}}}}}(\theta_{\Psi_{\text{CA}_{\vartheta_{\omega^{\chi_{\Phi_{\({\underbrace{\Omega_{\Omega_{\Omega_{._{._{._{\Omega}}}}}}}_{F_{7}{\Omega’s}}}\)_{I+I+I\cdots+I+1_{\({\underbrace{M({M({M({\cdots({M({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{M’s}}}\)_{\({\underbrace{K({K({K({\cdots({K({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{K’s}}}\)}}}}}}}}}})}(\chi_{\Phi_{ {\text{CA} _{\theta_{\Psi_{\vartheta_{\omega^{\epsilon_{\zeta_{\eta_{\Gamma_{\({\underbrace{\Omega_{\Omega_{\Omega_{._{._{._{\Omega}}}}}}}_{F_{7}{\Omega’s}}}\)_{\({\underbrace{I({I({I({\cdots({I({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{I’s}}}\)_{\({\underbrace{M({M({M({\cdots({M({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{M’s}}}\)_{\({\underbrace{K({K({K({\cdots({K({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{K’s}}}\)}}}}}}}}}}}}}}})(\theta_{\Psi_{\text{CA}_{\vartheta_{\omega^{\chi_{\Phi_{\Omega_{\Omega_{\Omega_{._{._{._{\Omega_{\({\underbrace{I({I({I({\cdots({I({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{I’s}}}\)_{\({\underbrace{M({M({M({\cdots({M({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{M’s}}}\)_{\({\underbrace{K({K({K({\cdots({K({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{K’s}}}\)}}}}}}}}}}}}}}}}})}}}}}}+1 \rightarrow \cdots\cdots \rightarrow {\text{CA} _{\theta_{\Psi_{\vartheta_{\omega^{\epsilon_{\zeta_{\eta_{\Gamma_{\psi_{\chi_{\Phi_{\({\underbrace{\Omega_{\Omega_{\Omega_{._{._{._{\Omega}}}}}}}_{F_{7}{\Omega’s}}}\)_{\({\underbrace{I({I({I({\cdots({I({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{I’s}}}\)_{\({\underbrace{M({M({M({\cdots({M({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{M’s}}}\)_{\({\underbrace{K({K({K({\cdots({K({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{K’s}}}\)}}}}}}}}(\theta_{\Psi_{\text{CA}_{\vartheta_{\omega^{\chi_{\Phi_{\({\underbrace{\Omega_{\Omega_{\Omega_{._{._{._{\Omega}}}}}}}_{F_{7}{\Omega’s}}}\)_{\({\underbrace{I({I({I({\cdots({I({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{I’s}}}\)_{\({\underbrace{M({M({M({\cdots({M({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{M’s}}}\)_{\({\underbrace{K({K({K({\cdots({K({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{K’s}}}\)}}}}}}}}}})}(\theta_{\Psi_{\text{CA}_{\chi_{\Phi_{ {\vartheta_{\omega^{\epsilon_{\zeta_{\eta_{\Gamma_{\({\underbrace{\Omega_{\Omega_{\Omega_{._{._{._{\Omega}}}}}}}_{F_{7}{\Omega’s}}}\)_{\({\underbrace{I({I({I({\cdots({I({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{I’s}}}\)_{\({\underbrace{M({M({M({\cdots({M({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{M’s}}}\)_{\({\underbrace{K({K({K({\cdots({K({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{K’s}}}\)}}}}}}}}}}}}}}})(\theta_{\Psi_{\text{CA}_{\vartheta_{\omega^{\chi_{\Phi_{\({\underbrace{\Omega_{\Omega_{\Omega_{._{._{._{\Omega}}}}}}}_{F_{7}{\Omega’s}}}\)_{\({\underbrace{I({I({I({\cdots({I({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{I’s}}}\)_{\({\underbrace{M({M({M({\cdots({M({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{M’s}}}\)_{\({\underbrace{K({K({K({\cdots({K({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{K’s}}}\)}}}}}}}}}}})}}}}}+\text{CA}_{n^{n+n^{n+n^{.^{.^{.^{n+n^{n+n}}}}}}}}}+\text{CA}^{BI}+1^{\text{CK}}}(\ \(f_\Sigma(f_\zeta(f_\gamma(f_\lambda(n \rightarrow n+n^{\text{CA}^{\text{BI}}})))) \rightarrow \({\underbrace{C({C({C({\cdots({C({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{C’s}}}\)

\(f_{\mu}=f_{\begin{pmatrix} f_{{\underbrace{C({C({C({\cdots({C({f{\varphi(f,f,f,\cdots \cdots,f)}(n)},0)},\cdots)},0)},0)},0)}_{f_{\varphi(f,f,f,\cdots \cdots,f)}(n){C’s}}}}(f) & f_{{\underbrace{C({C({C({\cdots({C({f_{\varphi(f,f,f,\cdots \cdots,f)}(n)},0)},\cdots)},0)},0)},0)}_{f_{\varphi(f,f,f,\cdots \cdots,f)}(n){C’s}}}}(f) & f_{{\underbrace{C({C({C({\cdots({C({f_{\varphi(f,f,f,\cdots \cdots,f)}(n)},0)},\cdots)},0)},0)},0)}_{f_{\varphi(f,f,f,\cdots \cdots,f)}(n){C’s}}}}(f) & \cdots & f_{{\underbrace{C({C({C({\cdots({C({f_{\varphi(f,f,f,\cdots \cdots,f)}(n)},0)},\cdots)},0)},0)},0)}_{f_{\varphi(f,f,f,\cdots \cdots,f)}(n){C’s}}}}(f)\\ f_{{\underbrace{C({C({C({\cdots({C({f_{\varphi(f,f,f,\cdots \cdots,f)}(n)},0)},\cdots)},0)},0)},0)}_{f_{\varphi(f,f,f,\cdots \cdots,f)}(n){C’s}}}}(f) & f_{{\underbrace{C({C({C({\cdots({C({f_{\varphi(f,f,f,\cdots \cdots,f)}(n)},0)},\cdots)},0)},0)},0)}_{f_{\varphi(f,f,f,\cdots \cdots,f)}(n){C’s}}}}(f) & f_{{\underbrace{C({C({C({\cdots({C({f_{\varphi(f,f,f,\cdots \cdots,f)}(n)},0)},\cdots)},0)},0)},0)}_{f_{\varphi(f,f,f,\cdots \cdots,f)}(n){C’s}}}}(f) & \cdots & f_{{\underbrace{C({C({C({\cdots({C({f_{\varphi(f,f,f,\cdots \cdots,f)}(n)},0)},\cdots)},0)},0)},0)}_{f_{\varphi(f,f,f,\cdots \cdots,f)}(n){C’s}}}}(f) \\ f_{{\underbrace{C({C({C({\cdots({C({f_{\varphi(f,f,f,\cdots \cdots,f)}(n)},0)},\cdots)},0)},0)},0)}_{f_{\varphi(f,f,f,\cdots \cdots,f)}(n){C’s}}}}(f) & f_{{\underbrace{C({C({C({\cdots({C({f_{\varphi(f,f,f,\cdots \cdots,f)}(n)},0)},\cdots)},0)},0)},0)}_{f_{\varphi(f,f,f,\cdots \cdots,f)}(n){C’s}}}}(f) & f_{{\underbrace{C({C({C({\cdots({C({f_{\varphi(f,f,f,\cdots \cdots,f)}(n)},0)},\cdots)},0)},0)},0)}_{f_{\varphi(f,f,f,\cdots \cdots,f)}(n){C’s}}}}(f) & \cdots & f_{{\underbrace{C({C({C({\cdots({C({f_{\varphi(f,f,f,\cdots \cdots,f)}(n)},0)},\cdots)},0)},0)},0)}_{f_{\varphi(f,f,f,\cdots \cdots,f)}(n){C’s}}}}(f) & f_{{\underbrace{C({C({C({\cdots({C({f_{\varphi(f,f,f,\cdots \cdots,f)}(n)},0)},\cdots)},0)},0)},0)}_{f_{\varphi(f,f,f,\cdots \cdots,f)}(n){C’s}}}}(f) & f_{{\underbrace{C({C({C({\cdots({C({f_{\varphi(f,f,f,\cdots \cdots,f)}(n)},0)},\cdots)},0)},0)},0)}_{f_{\varphi(f,f,f,\cdots \cdots,f)}(n){C’s}}}}(f) & \cdots & f_{{\underbrace{C({C({C({\cdots({C({f_{\varphi(f,f,f,\cdots \cdots,f)}(n)},0)},\cdots)},0)},0)},0)}_{f_{\varphi(f,f,f,\cdots \cdots,f)}(n){C’s}}}}(f) \\ \cdots \\ f_{{\underbrace{C({C({C({\cdots({C({f_{\varphi(f,f,f,\cdots \cdots,f)}(n)},0)},\cdots)},0)},0)},0)}_{f_{\varphi(f,f,f,\cdots \cdots,f)}(n){C’s}}}}(f) & f_{{\underbrace{C({C({C({\cdots({C({f_{\varphi(f,f,f,\cdots \cdots,f)}(n)},0)},\cdots)},0)},0)},0)}_{f_{\varphi(f,f,f,\cdots \cdots,f)}(n){C’s}}}}(f) & f_{{\underbrace{C({C({C({\cdots({C({f_{\varphi(f,f,f,\cdots \cdots,f)}(n)},0)},\cdots)},0)},0)},0)}_{f_{\varphi(f,f,f,\cdots \cdots,f)}(n){C’s}}}}(f) & \cdots & f_{{\underbrace{C({C({C({\cdots({C({f_{\varphi(f,f,f,\cdots \cdots,f)}(n)},0)},\cdots)},0)},0)},0)}_{f_{\varphi(f,f,f,\cdots \cdots,f)}(n){C’s}}}}(f)\\ f_{{\underbrace{C({C({C({\cdots({C({f_{\varphi(f,f,f,\cdots \cdots,f)}(n)},0)},\cdots)},0)},0)},0)}_{f_{\varphi(f,f,f,\cdots \cdots,f)}(n){C’s}}}}(f) & f_{{\underbrace{C({C({C({\cdots({C({f_{\varphi(f,f,f,\cdots \cdots,f)}(n)},0)},\cdots)},0)},0)},0)}_{f_{\varphi(f,f,f,\cdots \cdots,f)}(n){C’s}}}}(f) & f_{{\underbrace{C({C({C({\cdots({C({f_{\varphi(f,f,f,\cdots \cdots,f)}(n)},0)},\cdots)},0)},0)},0)}_{f_{\varphi(f,f,f,\cdots \cdots,f)}(n){C’s}}}}(f) & \cdots & f_{{\underbrace{C({C({C({\cdots({C({f_{\varphi(f,f,f,\cdots \cdots,f)}(n)},0)},\cdots)},0)},0)},0)}_{f_{\varphi(f,f,f,\cdots \cdots,f)}(n){C’s}}}}(f)\end{pmatrix} }(f)\)

\(f_{\omega}= n= f_{\alpha} ^{f_{\mu}}\underbrace{\uparrow\ldots\uparrow}_{f_{\alpha} ^{f_{\mu}}} f_{\alpha} ^{f_{\mu}},f_\Sigma(f_\zeta(f_\gamma(f_\lambda(F^{\Pi^(f_\Sigma(f_\zeta(f_\gamma(f_\lambda({\text{CA}_{n+3^{n+3^{n+3^{.^{.^{.^{n+3^{1+3}}}}}}} \rightarrow n+3^{n+3^{n+3^{.^{.^{.^{n+3^{2+3}}}}}}} \rightarrow n+3^{n+3^{n+3^{.^{.^{.^{n+3^{3+3}}}}}}} \cdots\cdots \rightarrow n+3^{n+3^{n+3^{.^{.^{.^{n+3^{n+3}}}}}}}+n+{\text{CA}^{\text{BI}^{n+{\text{CA}^{\text{BI}^{n+{\text{CA}^{\text{BI}^{.^{.^{.^{n+{\text{CA} ^{\text{BI}}}}}}}}}}}}}}}}}_ (f_\Sigma(f_\zeta(f_\gamma(f_\lambda({\text{CA}_{n+3^{n+3^{n+3^{.^{.^{.^{n+3^{1+3}}}}}}} \rightarrow n+3^{n+3^{n+3^{.^{.^{.^{n+3^{2+3}}}}}}} \rightarrow n+3^{n+3^{n+3^{.^{.^{.^{n+3^{3+3}}}}}}} \cdots\cdots \rightarrow n+3^{n+3^{n+3^{.^{.^{.^{n+3^{n+3}}}}}}}+n+{\text{CA} ^{\text{BI}^{n+{\text{CA}^{\text{BI}^{n+{\text{CA}^{\text{BI}^{.^{.^{.^{n+{\text{CA}^{\text{BI}}}}}}}}}}}}}}}}}}_ (f_\Sigma(f_\zeta(f_\gamma(f_\lambda(f^{\Pi^{\text{CA}_{n+3^{n+3^{n+3^{.^{.^{.^{n+3^{1+3}}}}}}} \rightarrow n+3^{n+3^{n+3^{.^{.^{.^{n+3^{2+3}}}}}}} \rightarrow n+3^{n+3^{n+3^{.^{.^{.^{n+3^{3+3}}}}}}} \cdots\cdots \rightarrow n+3^{n+3^{n+3^{.^{.^{.^{n+3^{n+3}}}}}}}+n+{\text{CA}^{\text{BI}^{n+{\text{CA}^{\text{BI}^{n+{\text{CA}^{\text{BI}^{.^{.^{.^{n+{\text{CA} ^{\text{BI}}}}}}}}}}}}}}}}}_{\text{CA}_{n+3^{n+3^{n+3^{.^{.^{.^{n+3^{1+3}}}}}}} \rightarrow n+3^{n+3^{n+3^{.^{.^{.^{n+3^{2+3}}}}}}} \rightarrow n+3^{n+3^{n+3^{.^{.^{.^{n+3^{3+3}}}}}}} \cdots\cdots \rightarrow n+3^{n+3^{n+3^{.^{.^{.^{n+3^{n+3}}}}}}}+n+{\text{CA} ^{\text{BI}^{n+{\text{CA}^{\text{BI}^{n+{\text{CA}^{\text{BI}^{.^{.^{.^{n+{\text{CA}^{\text{BI}}}}}}}}}}}}}}}}}}_{\omega_{\theta_{\Psi_{\text{CA}_{\vartheta_{\omega^{\epsilon_{\zeta_{\eta_{\Gamma_{\psi_{\chi_{\Phi_{\({\underbrace{\Omega_{\Omega_{\Omega_{._{._{._{\Omega}}}}}}}_{F_{7}{\Omega’s}}}\)_{\({\underbrace{I({I({I({\cdots({I({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{I’s}}}\)_{\({\underbrace{M({M({M({\cdots({M({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{M’s}}}\)_{\({\underbrace{K({K({K({\cdots({K({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{K’s}}}\)}}}}}}}}}text{CA} _{\theta_{\Psi_{\vartheta_{\omega^{\chi_{\Phi_{\({\underbrace{\Omega_{\Omega_{\Omega_{._{._{._{\Omega}}}}}}}_{F_{7}{\Omega’s}}}\)_{\({\underbrace{I({I({I({\cdots({I({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{I’s}}}\)_{\({\underbrace{M({M({M({\cdots({M({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{M’s}}}\)_{\({\underbrace{K({K({K({\cdots({K({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{K’s}}}\)}}}}}}}}}})}(\theta_{\Psi_{\text{CA}_{\Psi_{\chi_{\Phi_{ {\vartheta_{\omega^{\epsilon_{\zeta_{\eta_{\Gamma_{\({\underbrace{\Omega_{\Omega_{\Omega_{._{._{._{\Omega}}}}}}}_{F_{7}{\Omega’s}}}\)_{\({\underbrace{I({I({I({\cdots({I({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{I’s}}}\)_{\({\underbrace{M({M({M({\cdots({M({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{M’s}}}\)_{\({\underbrace{K({K({K({\cdots({K({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{K’s}}}\)}}}}}}}}}}}}}}})(\text{CA} _{\theta_{\vartheta_{\omega^{\chi_{\Phi_{\Omega_{\Omega_{\Omega_{._{._{._{\Omega_{\({\underbrace{I({I({I({\cdots({I({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{I’s}}}\)_{\({\underbrace{M({M({M({\cdots({M({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{M’s}}}\)_{\({\underbrace{K({K({K({\cdots({K({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{K’s}}}\)}}}}}}}}}}}}}}}})}}}}}}+1 \rightarrow {\text{CA} _{\theta_{\Psi_{\vartheta_{\omega^{\epsilon_{\zeta_{\eta_{\Gamma_{\psi_{\chi_{\Phi_{\({\underbrace{\Omega_{\Omega_{\Omega_{._{._{._{\Omega}}}}}}}_{F_{7}{\Omega’s}}}\)_{\({\underbrace{I({I({I({\cdots({I({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{I’s}}}\)_{\({\underbrace{M({M({M({\cdots({M({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{M’s}}}\)_{\({\underbrace{K({K({K({\cdots({K({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{K’s}}}\)}}}}}}}}}(\theta_{\Psi_{\text{CA}_{\vartheta_{\omega^{\chi_{\Phi_{\({\underbrace{\Omega_{\Omega_{\Omega_{._{._{._{\Omega}}}}}}}_{F_{7}{\Omega’s}}}\)_{\({\underbrace{I({I({I({\cdots({I({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{I’s}}}\)_{\({\underbrace{M({M({M({\cdots({M({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{M’s}}}\)_{\({\underbrace{K({K({K({\cdots({K({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{K’s}}}\)}}}}}}}}}})}(\theta_{\Psi_{\text{CA}_{\chi_{\Phi_{ {\vartheta_{\omega^{\epsilon_{\zeta_{\eta_{\Gamma_{\({\underbrace{\Omega_{\Omega_{\Omega_{._{._{._{\Omega}}}}}}}_{F_{7}{\Omega’s}}}\)_{\({\underbrace{I({I({I({\cdots({I({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{I’s}}}\)_{\({\underbrace{M({M({M({\cdots({M({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{M’s}}}\)_{\({\underbrace{K({K({K({\cdots({K({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{K’s}}}\)}}}}}}}}}}}}}})(\theta_{\Psi_{\text{CA}_{\vartheta_{\omega^{\chi_{\Phi_{\Omega_{\Omega_{\Omega_{._{._{._{\Omega_{\({\underbrace{I({I({I({\cdots({I({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{I’s}}}\)_{\({\underbrace{M({M({M({\cdots({M({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{M’s}}}\)_{\({\underbrace{K({K({K({\cdots({K({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{K’s}}}\)}}}}}}}}}}}}}}}}})}}}}}}+1 \rightarrow {\text{CA} _{\theta_{\Psi_{\vartheta_{\omega^{\epsilon_{\zeta_{\eta_{\Gamma_{\psi_{\chi_{\Phi_{\({\underbrace{\Omega_{\Omega_{\Omega_{._{._{._{\Omega}}}}}}}_{F_{7}{\Omega’s}}}\)_{\({\underbrace{I({I({I({\cdots({I({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{I’s}}}\)_{\({\underbrace{M({M({M({\cdots({M({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{M’s}}}\)_{\({\underbrace{K({K({K({\cdots({K({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{K’s}}}\)}}}}}}}}(\theta_{\Psi_{\text{CA}_{\vartheta_{\omega^{\chi_{\Phi_{\({\underbrace{\Omega_{\Omega_{\Omega_{._{._{._{\Omega}}}}}}}_{F_{7}{\Omega’s}}}\)_{I+I+I\cdots+I+1_{\({\underbrace{M({M({M({\cdots({M({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{M’s}}}\)_{\({\underbrace{K({K({K({\cdots({K({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{K’s}}}\)}}}}}}}}}})}(\chi_{\Phi_{ {\text{CA} _{\theta_{\Psi_{\vartheta_{\omega^{\epsilon_{\zeta_{\eta_{\Gamma_{\({\underbrace{\Omega_{\Omega_{\Omega_{._{._{._{\Omega}}}}}}}_{F_{7}{\Omega’s}}}\)_{\({\underbrace{I({I({I({\cdots({I({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{I’s}}}\)_{\({\underbrace{M({M({M({\cdots({M({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{M’s}}}\)_{\({\underbrace{K({K({K({\cdots({K({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{K’s}}}\)}}}}}}}}}}}}}}})(\theta_{\Psi_{\text{CA}_{\vartheta_{\omega^{\chi_{\Phi_{\Omega_{\Omega_{\Omega_{._{._{._{\Omega_{\({\underbrace{I({I({I({\cdots({I({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{I’s}}}\)_{\({\underbrace{M({M({M({\cdots({M({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{M’s}}}\)_{\({\underbrace{K({K({K({\cdots({K({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{K’s}}}\)}}}}}}}}}}}}}}}}})}}}}}}+1 \rightarrow \cdots\cdots \rightarrow {\text{CA} _{\theta_{\Psi_{\vartheta_{\omega^{\epsilon_{\zeta_{\eta_{\Gamma_{\psi_{\chi_{\Phi_{\({\underbrace{\Omega_{\Omega_{\Omega_{._{._{._{\Omega}}}}}}}_{F_{7}{\Omega’s}}}\)_{\({\underbrace{I({I({I({\cdots({I({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{I’s}}}\)_{\({\underbrace{M({M({M({\cdots({M({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{M’s}}}\)_{\({\underbrace{K({K({K({\cdots({K({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{K’s}}}\)}}}}}}}}(\theta_{\Psi_{\text{CA}_{\vartheta_{\omega^{\chi_{\Phi_{\({\underbrace{\Omega_{\Omega_{\Omega_{._{._{._{\Omega}}}}}}}_{F_{7}{\Omega’s}}}\)_{\({\underbrace{I({I({I({\cdots({I({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{I’s}}}\)_{\({\underbrace{M({M({M({\cdots({M({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{M’s}}}\)_{\({\underbrace{K({K({K({\cdots({K({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{K’s}}}\)}}}}}}}}}})}(\theta_{\Psi_{\text{CA}_{\chi_{\Phi_{ {\vartheta_{\omega^{\epsilon_{\zeta_{\eta_{\Gamma_{\({\underbrace{\Omega_{\Omega_{\Omega_{._{._{._{\Omega}}}}}}}_{F_{7}{\Omega’s}}}\)_{\({\underbrace{I({I({I({\cdots({I({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{I’s}}}\)_{\({\underbrace{M({M({M({\cdots({M({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{M’s}}}\)_{\({\underbrace{K({K({K({\cdots({K({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{K’s}}}\)}}}}}}}}}}}}}}})(\theta_{\Psi_{\text{CA}_{\vartheta_{\omega^{\chi_{\Phi_{\({\underbrace{\Omega_{\Omega_{\Omega_{._{._{._{\Omega}}}}}}}_{F_{7}{\Omega’s}}}\)_{\({\underbrace{I({I({I({\cdots({I({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{I’s}}}\)_{\({\underbrace{M({M({M({\cdots({M({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{M’s}}}\)_{\({\underbrace{K({K({K({\cdots({K({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{K’s}}}\)}}}}}}}}}}})}}}}}+\text{CA}_{n^{n+n^{n+n^{.^{.^{.^{n+n^{n+n}}}}}}}}}+\text{CA}^{BI}+1^{\text{CK}}}(\ \(f_\Sigma(f_\zeta(f_\gamma(f_\lambda(n \rightarrow n+n^{\text{CA}^{\text{BI}}})))) \rightarrow \({\underbrace{C({C({C({\cdots({C({F_{7}},0)},\cdots)},0)},0)},0)}_{F_{7}{C’s}}}\)