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
See also
- Ultra Psi Notation