FANDOM


Rule 1: If there is nothing after the colon, the result is the number before the colon

Rule 2: If the expression ends in a bracket psir

Rule 2a: If the only entry of it is 0, add 1 to the number beforte the colon

Rule 3: If the expression ends in a star level 1, copy the expression before the colon and after the last bracket copies of the expression without the star

Rule 4: If the epression ends in a star level 2 or greater, decrement the level of that star by one and copy it the number before the bracket times.



Example: 2:[0]**

=2:[0]*[0]*

=2:[0]*[0][0]

=3:[0]*[0]

=4:[0]*

=4:[0][0][0][0]

=5:[0][0][0]

=6:[0][0]

=7:[0]

=8:

=8

3:[0]*3

=3:[0]*2*2*2

=3:[0]*2*2***

=3:[0]*2*2**[0]*2*2**[0]*2*2**

=3:[0]*2*2**[0]*2*2**[0]*2*2*[0]*2*2*[0]*2*2*

=3:[0]*2*2**[0]*2*2**[0]*2*2*[0]*2*2*[0]*2*2[0]*2*2[0]*2*2

=3:[0]*2*2**[0]*2*2**[0]*2*2*[0]*2*2*[0]*2*2[0]*2*2[0]*2***

=3:[0]*2*2**[0]*2*2**[0]*2*2*[0]*2*2*[0]*2*2[0]*2*2[0]*2**[0]*2**[0]*2**

=3:[0]*2*2**[0]*2*2**[0]*2*2*[0]*2*2*[0]*2*2[0]*2*2[0]*2**[0]*2**[0]*2*[0]*2*[0]*2*

=3:[0]*2*2**[0]*2*2**[0]*2*2*[0]*2*2*[0]*2*2[0]*2*2[0]*2**[0]*2**[0]*2*[0]*2*[0]*2[0]*2[0]*2

=3:[0]*2*2**[0]*2*2**[0]*2*2*[0]*2*2*[0]*2*2[0]*2*2[0]*2**[0]*2**[0]*2*[0]*2*[0]*2[0]*2[0]***

=3:[0]*2*2**[0]*2*2**[0]*2*2*[0]*2*2*[0]*2*2[0]*2*2[0]*2**[0]*2**[0]*2*[0]*2*[0]*2[0]*2[0]**[0]**[0]**

=3:[0]*2*2**[0]*2*2**[0]*2*2*[0]*2*2*[0]*2*2[0]*2*2[0]*2**[0]*2**[0]*2*[0]*2*[0]*2[0]*2[0]**[0]**[0]*[0]*[0]*

=3:[0]*2*2**[0]*2*2**[0]*2*2*[0]*2*2*[0]*2*2[0]*2*2[0]*2**[0]*2**[0]*2*[0]*2*[0]*2[0]*2[0]**[0]**[0]*[0]*[0][0][0]

=4:[0]*2*2**[0]*2*2**[0]*2*2*[0]*2*2*[0]*2*2[0]*2*2[0]*2**[0]*2**[0]*2*[0]*2*[0]*2[0]*2[0]**[0]**[0]*[0]*[0][0]

=5:[0]*2*2**[0]*2*2**[0]*2*2*[0]*2*2*[0]*2*2[0]*2*2[0]*2**[0]*2**[0]*2*[0]*2*[0]*2[0]*2[0]**[0]**[0]*[0]*[0]

=6:[0]*2*2**[0]*2*2**[0]*2*2*[0]*2*2*[0]*2*2[0]*2*2[0]*2**[0]*2**[0]*2*[0]*2*[0]*2[0]*2[0]**[0]**[0]*[0]*

=6:[0]*2*2**[0]*2*2**[0]*2*2*[0]*2*2*[0]*2*2[0]*2*2[0]*2**[0]*2**[0]*2*[0]*2*[0]*2[0]*2[0]**[0]**[0]*[0][0][0][0][0][0]

=7:[0]*2*2**[0]*2*2**[0]*2*2*[0]*2*2*[0]*2*2[0]*2*2[0]*2**[0]*2**[0]*2*[0]*2*[0]*2[0]*2[0]**[0]**[0]*[0][0][0][0][0]

=8:[0]*2*2**[0]*2*2**[0]*2*2*[0]*2*2*[0]*2*2[0]*2*2[0]*2**[0]*2**[0]*2*[0]*2*[0]*2[0]*2[0]**[0]**[0]*[0][0][0][0]

=9:[0]*2*2**[0]*2*2**[0]*2*2*[0]*2*2*[0]*2*2[0]*2*2[0]*2**[0]*2**[0]*2*[0]*2*[0]*2[0]*2[0]**[0]**[0]*[0][0][0]

=10:[0]*2*2**[0]*2*2**[0]*2*2*[0]*2*2*[0]*2*2[0]*2*2[0]*2**[0]*2**[0]*2*[0]*2*[0]*2[0]*2[0]**[0]**[0]*[0][0]

=11:[0]*2*2**[0]*2*2**[0]*2*2*[0]*2*2*[0]*2*2[0]*2*2[0]*2**[0]*2**[0]*2*[0]*2*[0]*2[0]*2[0]**[0]**[0]*[0]

=12:[0]*2*2**[0]*2*2**[0]*2*2*[0]*2*2*[0]*2*2[0]*2*2[0]*2**[0]*2**[0]*2*[0]*2*[0]*2[0]*2[0]**[0]**[0]*


Analisys

n:[0]=f0(n)

n:[0][0]=f0(f0(n))

n:[0]*=f1(n)

n:[0]*=f1(n)

n:[0]*[0]=f1(f0(n))

n:[0]*[0]*=f1(f1(n))

n:[0]**=f2(n)

n:[0]***=f3(n)

n:[0]*2=fw(n)

n:[0]*2*=fw+1(n)

n:[0]*2*2=fw2(n)

n:[0]*2*2*2=fw3(n)

n:[0]*3=fw^2(n)

n:[0]*4=fw^3(n)

n:[0]*n=fw^n-1(n)


Let's allow you to nest expressions.

n:[0]*2=n:[0]*[0]

n:[0]*3=n:[0]*[0][0]

n:[0]*3=n:[0]*[0][0][0]

n:[0]*[0]*=fw^w(n)

n:[0]*[0]*[0]=fw^(w+1)(n)

n:[0]*[0]*[0]*=fw^(w*2)(n)

n:[0]*[0]**=fw^(w^2)(n)

n:[0]*[0]**=fw^(w^2)(n)

n:[0]*[0]***=fw^(w^3)(n)

n:[0]*[0]*2=fw^(w^w)(n)

n:[0]*[0]*2*=fw^(w^(w+1))(n)

n:[0]*[0]*2**=fw^(w^(w+2))(n)

n:[0]*[0]*2*2=fw^(w^(w2))(n)

n:[0]*[0]*2*2*2=fw^(w^(w3))(n)

n:[0]*[0]*3=fw^(w^(w^2))(n)

n:[0]*[0]*4=fw^(w^(w^3))(n)

n:[0]*[0]*[0]*=fw^(w^(w^w))(n)

n:[0]*[0]*[0]*2=fw^(w^(w^(w^w)))(n)

n:[0]*[0]*[0]*[0]*=fw^(w^(w^(w^(w^w))))(n)

Let's have [0]/ be the fixed point of the function a -> [0]*a

n:[0]/=fe0(n)

n:[0]/*=fe0+1(n)

n:[0]/**=fe0+2(n)

n:[0]/*2=fe0+w(n)

n:[0]/*[0]*=fe0+w^w(n)

n:[0]/*[0]*=fe0+w^w(n)

n:[0]/*[0]*=fe0*2(n)

n:[0]/*[0]/*[0]=fe0*w(n)

n:[0]/*[0]/*[0]*=fe0*w^w(n)

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