## FANDOM

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Here a example : $$f_{\omega+2}(6)$$.

$$f_{\omega+2}(6)$$ =

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

$$f_{\omega+1}(f_{\omega+1}(f_{\omega+1}(f_{\omega+1}(f_{\omega+1}(f_{\omega+1}(6))))))$$ =

$$f_{\omega+1}(f_{\omega+1}(f_{\omega+1}(f_{\omega+1}(f_{\omega+1}(A)))))$$, this function get too complex so here a A:

$$f_{\omega+1}(6)$$ =

$$f_{\omega}^6(6)$$ =

$$f_{\omega}(f_{\omega}(f_{\omega}(f_{\omega}(f_{\omega}(f_{\omega}(6))))))$$ =

$$f_{\omega}(f_{\omega}(f_{\omega}(f_{\omega}(f_{\omega}(f_{6}(6))))))$$ =

$$f_{\omega}(f_{\omega}(f_{\omega}(f_{\omega}(f_{\omega}(B)))))$$, also A function get too complex so here a B:

$$f_{6}(6)$$ =

$$f_{5}^6(6)$$ =

$$f_{5}(f_{5}(f_{5}(f_{5}(f_{5}(f_{5}(6))))))$$.

So $$f_{\omega+2}(6)$$ > $$\{6,6,2,2\}$$.