## FANDOM

10,824 Pages

Rules: Rule 1: If there is nothing after the percent sign, the number before the percent sign is the answer

Rule 2: If the expression ends in a star sign, copy the expression before that the number before the percent sign times<

Rule 3: If the expression ends in a carat

Rule 3a: If the carat does not have a level, replace it with the number before the percent sign stars

Rule 3b: If the level is a number, make it the number before the percent sign slashes with the level decreased by one.

Rule 3c: If the level is an expression, solve it like normally and if it ends in a bracket with just a zero, copy that slash sign the number before the percent sign times.

Rule 3d, If the level is just a percent sign, replace it with the number before the percent sign.

Rule 4: If the expression ends in brackets:

Rule 4a: If the only entry is zero, add one to the number before the percent sign and removre those brackets

## Analysis

n%[0]=f_0(n)

n%[0]*=f_1(n)

n%[0]*[0]=f_1(n+1)

n%[0]*[0]*=f_1(f_1(n))

n%[0]**=f_2(n)

n%[0]**[0]=f_2(f_0(n))

n%[0]**[0]*=f_2(f_1(n))

n%[0]**[0]**=f_2(f_2(n))

n%[0]***=f_3(n)

n%[0]****=f_4(n)

n%[0]^=f_{\omega}(n)

n%[0]^*=f_{\omega+1}(n)

n%[0]^^=f_{\omega2}(n)

n%[0]^^^=f_{\omega3}(n)

n%[0]^2=f_{\omega^2}(n) ... ... n%[0]^n=f_{\omega^{\omega}}(n) n%[0]^[0]=f_{\omega^{\omega+1}}(n) n%

[0]^[0]*=f_{\omega^{\omega2}}(n) n%[0]^[0]*[0]=f_{\omega^{\omega2+1}}(n) n%[0]^[0]*[0]*=f_{\omega^{\omega3}}

(n) ... n%[0]^[0]**=f_{\omega^{\omega^2}}(n) n%[0]^[0]**[0]**=f_{\omega^{\omega^2}2}(n) n%

[0]^[0]***=f_{\omega^{\omega^3}}(n) n%[0]^[0]^=f_{\omega^{\omega^{\omega}}}(n) n%

[0]^[0]^*=f_{\omega^{\omega^{\omega+1}}}(n) n%[0]^[0]^^=f_{\omega^{\omega^{\omega2}}}(n) n%

[0]^[0]^2=f_{\omega^{\omega^{\omega^2}}}(n)

...

n%[0]/=f_{\varepsilon_0}(n)