User:Tridecal

$$X^{X^{X^{X^{X^{X^{X^{X^{.^{.^{.}}}}}}}}}+1}$$ = $$f_{\omega^{\omega^{\epsilon_0+1}}}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}}^2(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+1}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+2}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+3}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+4}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+5}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+6}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+7}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+\omega}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+\omega+1}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+\omega+2}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+\omega+3}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+\omega2}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+\omega3}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+\omega4}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+\omega5}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+\omega^2}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+\omega^2+1}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+\omega^2+\omega}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+\omega^22}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+\omega^3}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+\omega^4}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+\omega^5}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+\omega^\omega}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+\omega^\omega+1}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+\omega^\omega+\omega}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+\omega^\omega2}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+\omega^{\omega+1}}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+\omega^{\omega2}}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+\omega^{\omega3}}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+\omega^{\omega4}}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+\omega^{\omega^2}}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+\omega^{\omega^2}2}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+\omega^{\omega^2+1}}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+\omega^{\omega^2+\omega}}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+\omega^{\omega^22}}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+\omega^{\omega^3}}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+\omega^{\omega^4}}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+\omega^{\omega^\omega}}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+\omega^{\omega^{\omega^2}}}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+\omega^{\omega^{\omega^\omega}}}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+\omega^{\omega^{\omega^{\omega^\omega}}}}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+\omega^{\omega^{\omega^{\omega^{\omega^\omega}}}}}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+\omega^{\omega^{\omega^{\omega^{\omega^{\omega^\omega}}}}}}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+\epsilon_0}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+\epsilon_0+1}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+\epsilon_0+2}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+\epsilon_02}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+\epsilon_03}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}+\omega^{\epsilon_02}}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}2}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}3}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}4}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}5}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}6}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}}7}(100)$$

$$X^{X^{X^{X^{X^{X^{X^{X^{.^{.^{.}}}}}}}}}+1}+1$$ = $$f_{\omega^{\omega^{\epsilon_0+1}+1}}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}+1}+\omega^{\omega^{\epsilon_0+1}}}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}+1}+\omega^{\omega^{\epsilon_0+1}}2}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}+1}+\omega^{\omega^{\epsilon_0+1}}3}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}+1}2}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}+1}3}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}+1}4}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}+1}5}(100)$$

$$X^{X^{X^{X^{X^{X^{X^{X^{.^{.^{.}}}}}}}}}+1}+2$$ = $$f_{\omega^{\omega^{\epsilon_0+1}+2}}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}+2}+\omega^{\omega^{\epsilon_0+1}}}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}+2}+\omega^{\omega^{\epsilon_0+1}+1}}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}+2}2}(100)$$

$$X^{X^{X^{X^{X^{X^{X^{X^{.^{.^{.}}}}}}}}}+1}+3$$ = $$f_{\omega^{\omega^{\epsilon_0+1}+3}}(100)$$

$$X^{X^{X^{X^{X^{X^{X^{X^{.^{.^{.}}}}}}}}}+1}+4$$ = $$f_{\omega^{\omega^{\epsilon_0+1}+4}}(100)$$

$$X^{X^{X^{X^{X^{X^{X^{X^{.^{.^{.}}}}}}}}}+1}+5$$ = $$f_{\omega^{\omega^{\epsilon_0+1}+5}}(100)$$

$$X^{X^{X^{X^{X^{X^{X^{X^{.^{.^{.}}}}}}}}}+1}+6$$ = $$f_{\omega^{\omega^{\epsilon_0+1}+6}}(100)$$

$$X^{X^{X^{X^{X^{X^{X^{X^{.^{.^{.}}}}}}}}}+1}+7$$ = $$f_{\omega^{\omega^{\epsilon_0+1}+7}}(100)$$

$$X^{X^{X^{X^{X^{X^{X^{X^{.^{.^{.}}}}}}}}}+1}+X$$ = $$f_{\omega^{\omega^{\epsilon_0+1}+\omega}}(100)$$

$$X^{X^{X^{X^{X^{X^{X^{X^{.^{.^{.}}}}}}}}}+1}+X+1$$ = $$f_{\omega^{\omega^{\epsilon_0+1}+\omega+1}}(100)$$

$$X^{X^{X^{X^{X^{X^{X^{X^{.^{.^{.}}}}}}}}}+1}+X+2$$ = $$f_{\omega^{\omega^{\epsilon_0+1}+\omega+2}}(100)$$

$$X^{X^{X^{X^{X^{X^{X^{X^{.^{.^{.}}}}}}}}}+1}+2X$$ = $$f_{\omega^{\omega^{\epsilon_0+1}+\omega2}}(100)$$

$$X^{X^{X^{X^{X^{X^{X^{X^{.^{.^{.}}}}}}}}}+1}+X^2$$ = $$f_{\omega^{\omega^{\epsilon_0+1}+\omega^2}}(100)$$

$$X^{X^{X^{X^{X^{X^{X^{X^{.^{.^{.}}}}}}}}}+1}+X^3$$ = $$f_{\omega^{\omega^{\epsilon_0+1}+\omega^3}}(100)$$

$$X^{X^{X^{X^{X^{X^{X^{X^{.^{.^{.}}}}}}}}}+1}+X^4$$ = $$f_{\omega^{\omega^{\epsilon_0+1}+\omega^4}}(100)$$

$$X^{X^{X^{X^{X^{X^{X^{X^{.^{.^{.}}}}}}}}}+1}+X^X$$ = $$f_{\omega^{\omega^{\epsilon_0+1}+\omega^\omega}}(100)$$

$$X^{X^{X^{X^{X^{X^{X^{X^{.^{.^{.}}}}}}}}}+1}+X^{X^2}$$ = $$f_{\omega^{\omega^{\epsilon_0+1}+\omega^{\omega^2}}}(100)$$

$$X^{X^{X^{X^{X^{X^{X^{X^{.^{.^{.}}}}}}}}}+1}+X^{X^X}$$ = $$f_{\omega^{\omega^{\epsilon_0+1}+\omega^{\omega^\omega}}}(100)$$

$$X^{X^{X^{X^{X^{X^{X^{X^{.^{.^{.}}}}}}}}}+1}+X^{X^{X^X}}$$ = $$f_{\omega^{\omega^{\epsilon_0+1}+\omega^{\omega^{\omega^\omega}}}}(100)$$

$$X^{X^{X^{X^{X^{X^{X^{X^{.^{.^{.}}}}}}}}}+1}+X^{X^{X^{X^X}}}$$ = $$f_{\omega^{\omega^{\epsilon_0+1}+\omega^{\omega^{\omega^{\omega^\omega}}}}}(100)$$

$$X^{X^{X^{X^{X^{X^{X^{X^{.^{.^{.}}}}}}}}}+1}+X^{X^{X^{X^{X^{X^{X^{X^{.^{.^{.}}}}}}}}}}}$$ = $$f_{\omega^{\omega^{\epsilon_0+1}+\epsilon_0}}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}+\epsilon_0}+\omega^{\omega^{\epsilon_0+1}}}(100)$$

$$f_{\omega^{\omega^{\epsilon_0+1}+\epsilon_0}+\omega^{\omega^{\epsilon_0+1}}2}(100)$$

$$X^{X^{X^{X^{X^{X^{X^{X^{.^{.^{.}}}}}}}}}+1}+X^{X^{X^{X^{X^{X^{X^{X^{.^{.^{.}}}}}}}}}}}$$ = $$f_{\omega^{\omega^{\epsilon_0+1}+\epsilon_0}2}(100)$$

$$X^{X^{X^{X^{X^{X^{X^{X^{.^{.^{.}}}}}}}}}+1}+X^{X^{X^{X^{X^{X^{X^{X^{.^{.^{.}}}}}}}}}}}$$ = $$f_{\omega^{\omega^{\epsilon_0+1}+\epsilon_0}3}(100)$$

$$X^{X^{X^{X^{X^{X^{X^{X^{.^{.^{.}}}}}}}}}+1}+2X^{X^{X^{X^{X^{X^{X^{X^{.^{.^{.}}}}}}}}}}}$$ = $$f_{\omega^{\omega^{\epsilon_0+1}+\epsilon_02}}(100)$$

$$X^{X^{X^{X^{X^{X^{X^{X^{.^{.^{.}}}}}}}}}+1}+3X^{X^{X^{X^{X^{X^{X^{X^{.^{.^{.}}}}}}}}}}}$$ = $$f_{\omega^{\omega^{\epsilon_0+1}+\epsilon_03}}(100)$$

$$X^{X^{X^{X^{X^{X^{X^{X^{.^{.^{.}}}}}}}}}+1}+4X^{X^{X^{X^{X^{X^{X^{X^{.^{.^{.}}}}}}}}}}}$$ = $$f_{\omega^{\omega^{\epsilon_0+1}+\epsilon_04}}(100)$$

$$2X^{X^{X^{X^{X^{X^{X^{X^{.^{.^{.}}}}}}}}}+1}$$ = $$f_{\omega^{\omega^{\epsilon_0+1}2}}(100)$$

$$3X^{X^{X^{X^{X^{X^{X^{X^{.^{.^{.}}}}}}}}}+1}$$ = $$f_{\omega^{\omega^{\epsilon_0+1}3}}(100)$$

$$4X^{X^{X^{X^{X^{X^{X^{X^{.^{.^{.}}}}}}}}}+1}$$ = $$f_{\omega^{\omega^{\epsilon_0+1}4}}(100)$$

$$5X^{X^{X^{X^{X^{X^{X^{X^{.^{.^{.}}}}}}}}}+1}$$ = $$f_{\omega^{\omega^{\epsilon_0+1}5}}(100)$$

$$6X^{X^{X^{X^{X^{X^{X^{X^{.^{.^{.}}}}}}}}}+1}$$ = $$f_{\omega^{\omega^{\epsilon_0+1}6}}(100)$$

$$X^{X^{X^{X^{X^{X^{X^{X^{.^{.^{.}}}}}}}}}+2}$$ = $$f_{\omega^{\omega^{\epsilon_0+2}}}(100)$$