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# New Definition of Oe and Os

$$f(n)=x$$, when $$(10\uparrow\uparrow n)^{10\uparrow\uparrow n}=(10\uparrow)^{n+2}x$$

• $$f(1,1)=f(54)$$ = Level 1
• $$f(1,a)=f(\frac{1}{f(1,a-1)})$$, Here $$\frac{1}{f(a-1)}$$ might not be integer, so round it off (and so forth).
• $$f(2,1)=f(1,54)$$
• $$f(2,a)=f(\frac{1}{f(1,a-1)})$$
• $$f(b,1)=f(b-1,54)$$
• $$f(b,n)=f(b-1,\frac{1}{f(b,n-1)})$$
• $$f(1,1,1)=f(54,1)$$ = Level 2
• $$f(1,1,a)=f(\frac{1}{f(1,1,a-1)},1)$$
• $$f(c,1,1)=f(c-1,54,1)$$
• $$f(c,1,a)=f(c-1,\frac{1}{f(c,1,a-1)},1)$$
• $$f(c,b,1)=f(c,b-1,54)$$
• $$f(c,b,a)=f(c,b-1,\frac{1}{f(c,b,a-1)})$$
• $$f(1,1,1,1)=f(54,1,1)$$ = Level 3
• $$f(1,1,1,1,1)=f(54,1,1,1)$$ = Level 4

...in general,

• $$f(1,1,\underbrace{1,\dots,1}_{n\text{ copies of }1}) = f(54,\underbrace{1,\dots,1}_{n\text{ copies of }1})$$
• $$f(1,1,\underbrace{1,\dots,1}_{n},a) = f(\frac{1}{f(1,1,\underbrace{1,\dots,1}_{n},a-1)},\underbrace{1,\dots,1}_{n},1)$$
• $$f(\dots,m,1,\underbrace{1,\dots,1}_{n}) = f(\dots,m-1,54,\underbrace{1,\dots,1}_{n})$$
• $$f(\dots,m,1,\underbrace{1,\dots,1}_{n},a) = f(\dots,m-1,\frac{1}{f(\dots,m,1,\underbrace{1,\dots,1}_{n},a-1)},\underbrace{1,\dots,1}_{n},1)$$
• $$f(\dots,b,1) = f(\dots,b-1,54)$$
• $$f(\dots,b,a) = f(\dots,b-1,\frac{1}{f(\dots,b,a-1)})$$
• and $$e(\underbrace{1,\dots,1}_{n+1})$$ = Level n = $$Oe(n)$$
• and when it reaches?$$Oe(54)$$, that is Okojo-ermine Number($$Oe$$)
• $$\frac{1}{Oe}$$ = Okojo-stoat Number($$Os$$), and $$\frac{1}{Oe(n)}=Os(n)$$

$$Os$$ might not be integer, but it doesn't need to be rounded off.

# Old Definition of Oe and Os

$$f(n)=x$$, when $$(10\uparrow\uparrow n)^{10\uparrow\uparrow n}=(10\uparrow)^n(10+x)$$

• $$A_{1,1}=f(54)$$ = Level 1
• $$A_{1,n}=f(\frac{1}{A_{1,n-1}})$$ if $$\frac{1}{A_{1,n-1}}$$ is not integer, so round it off (and so forth).
• $$A_{2,1}=A_{1,54}$$ = Level 2
• $$A_{m,1}=A_{m-1,54}$$
• $$A_{m,n}=A_{m-1,{\frac{1}{A{m,n-1}}}}$$
• $$B_{1,1,1}=A_{54,1}$$ = Level 3
• $$B_{1,1,n}=A_{\frac{1}{B{1,1,n-1}},1}$$
• $$B_{l,m,1}=B_{1,m-1,54}$$
• $$B_{l,m,n}=B_{l,m-1,{\frac{1}{B_{1,m,n-1}}}}$$
• $$B_{l,1,1}=B_{l-1,54,1}$$
• $$C_{1,1,1}=B_{54-1,1,1}$$ = Level 4
• $$C_{1,1,n}=B_{\frac{1}{C{1,1,n-1}}-1,1,1}$$
• $$C_{l,m,1}=C_{1,m-1,54}$$
• $$C_{l,m,n}=C_{l,m-1,{\frac{1}{C_{1,m,n-1}}}}$$
• $$C_{l,1,1}=C_{l-1,54,1}$$
• $$D_{1,1,1}=C_{54-1,1,1}$$ = Level 5
• Same as above
• $$E_{1,1,1}=D_{54-1,1,1}$$ = Level 6
• Same as above
• Level54 = Okojo-ermine Number, Level n = $$Oe(n)$$
• Okojo-ermine Number$$^{-1}$$ = Okojo-stoat Number , $$(Oe(n))^{-1}=Os(n)$$