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For psi functions, see ψ.

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