Psi Notation

The Psi Notation is a Googological Notation devised by Antares.I.G.Harrison. It's growth rate is not determined yet.

It was largely based on SAN and HAN.

Here are primes rules. They can be also found at Antares.I.G.Harrison's |Website.

- Prime Rules

1. Every Array/Integer - Every Array/Integer in the notation, the Psi (Ψ) is Needed. ( i.e. No Psi, then the whole array is wrong)

2. Only One Entry - Ψn = n^n

2-1. Psi-Related - Ψnm = m^mn

3. Arrays - n_m_...% (% is the rest of the array)

3-1. Array Rule - Always calcluate 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 - n_m_o = n^n^...^n (m_o times)

4. Cerncerning 1, 0, and Infinity

4-1. If 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 (i.e.Ψn_m_..._(Infinity)_..% = (Infinity))

4-4. Zero - Zeroes, like Infinity, in ANY array, will cause the array to become 1 (See i.e. on 4-3)

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. Extended Array Marks - ΨAAnm = ΨA(ΨAnm)m

5-3-3. Y Array - ΨYnm= ΨAA...AAnm

5-4. Bracker lines

5-5. Calculate the brackets first - Ψn_m/_m_n = Ψ(n_m)_(m_n)

5-6. "<>" Operators

5-6-1. Ψnm = 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 times)

5-7. n@ = n_n_..._n (n times)

6. Small Numbers

6-1. nm= Ψn_Ψn_Ψn_..._Ψn (m times)

7. Psi's

7-1. ΨΨn = Ψn_Ψn

7-2. ΨΨ...($ times)...Ψn = Ψn_Ψn_Ψn...Ψn ($ times) = $Ψn

7-2-1. nΨm ≠ n x Ψm


 * EXAMPLES*

Googol = Ψ1010 = 10^10x10 = 10^100

Tritri = Ψ3_3_3)

Decker = Ψ10_10

Gaggol = Ψ10#100

Googolplex ΨGoogol÷1010 = 10^10 x Googol÷10 = 10^Googol

=Citations=
 * |Antares.I.G.Harrison's Website