Psi Notation

Psi notation is a googological notation devised by Antares I.G. Harrison. Its growth rate is \(f_{\omega}(n)\), on par with up-arrow notation.
It was largely based on ExE and HAN.
== Rules ==
*1 Every array/integer - In every array/integer in the notation, the psi (Ψ) is needed.
*2. Only one entry:
**2-1. Ψn = nn
** 2-2. Ψnm = mmn
*3. Arrays - n_m_...% (% is the rest of the array)
**3-1. Array rule - Always calculate from the back
**3-2. Array rule - Any array calculates from the back.
**3-3. Prime array rule - n_m = n^n^n^...^n (m times) (tetration)
**3-4. 2<n array rule - %_m_n = %_(m_n)
*4. Concerning 1, 0, and Infinty
**4-1. If the expression is Ψn_m_1, the 1 may be cropped off (Ψn_m_1 = Ψn_m)
**4-2. Ψ1_n_% = 1
**4-3. Infinity - The presence of infinity anywhere will cause the whole array to turn into infinity.
**4-4. Zero - Zeroes, like infinity, in any array, will cause the array to become 1.
*5. Special delimeters
**5-1. Ψn#m = n_n_..._n (m times)
**5-2. Ψn? = n_(n-1)_(n-2)_..._2_1
**5-3. Array marks (A,Y) (Based on BEAF's legions)
***5-3-1. Simple array mark rules - Ψ (main) A (array leader) n (array base) m (array children)
***5-3-2. Y array - ΨYnm= ΨAA...AAnm
**5-4. Bracket lines
**5-5. Calculate the brackets first - Ψn_m/_m_n = Ψ(n_m)_(m_n)
**5-6. "<>" Operators
***5-6-1. Ψn<m = n#n#n...n#n (m times)
***5-6-2. Ψn>m = m#m#m#...#m (n times)
***5-6-3. Ψn>>m = n>n>n>...>n (m times)
***5-6-4. ΨnA<mo= Ψn<<<......<<<o (m copies of >)
**5-7. n@ = n_n_..._n (n times)
*6. Small numbers
*6-1. nm= Ψn_Ψn_Ψn_..._Ψn (m times)
*7. Psis
**7-1. ΨΨn = Ψn_Ψn
**7-2. ΨΨ...($ times)...Ψn = Ψn_Ψn_Ψn...Ψn ($ times) = $Ψn
***7-2-1. nΨm ≠ n x Ψm
This notation is currently under construction.
== Examples ==
Googol = Ψ1010 = 10^(10*10) = 10^100
Tritri = Ψ3_3_3
Decker = Ψ10_10
Gaggol = Ψ10#100
Googolplex = Ψ109910 = 1010*1099 = 1010100
== Sources ==
*Antares I.G. Harrison's Website
Category:Functions
Category:Notations