Greek letter notations extend chained arrow notation and themselves using the laws of recursion.

Conway Notation is used to build powers of up arrow notation when it gets cumbersome to handle. But what occurs when Conway Notation becomes too cumbersome to handle? Greek notation can help with this by building towers in a similar way as Conway Chains build up arrow towers.


The first Greek function is called Alpha Function, denoted with an A. A defines the instructions for building towers of Conway Notation. The first number in front of the A, called N, is the number repeated in the base of the Conway Tower an N amount of times. The number after the A, called X, defines the amount of towers of Conway Chains to build. For example, 5A1 means the following: 5->5->5->5->5 with one tower (so this is the correct expansion). Another example: 3A100 which is equal to 3->3->3...->3 with a 3A99 amount of chains in between. 3AA3 is 3A(3A(3A3))) using the rules of recursion. More advanced versions of A exist such as: 4AA(100)AA4 which contains 100 A's between the two 4s.

6th function is defined as beta. It does the same exact thing as A does to Conway Notation: 5B1 is 5AAAAA5, 3B100 is 3AA...AA3 with 3B99 A's in between. 3BB3 is 3B(3B(3B)), and 4BB(100)BB4 contains 100 A's between the two fours. 

Greek notation forms the basis of Notation Array Notation. The representation in NaN: 3A3 is (3{5,1}3) for the two 3s in the function, 5 for the level in which A is, and 1 is for having only one A. 3AA(100)AA3 is defined as (3{5,100}3). 3B3 is (3{6,1}3).  

This is how the notation is used: n,qAA...AAx where n is the number in the base, and q is the amount of that number in the base. If the two numbers are the same, you don't need the comma. The As represent the level of the notation. The 4 level in Conway Notation corresponds to one A in the alpha notation (so by adding one A you increase the tower in a compounded way similar to that which adding a fifth chain to Conway chain notation increases the amount of arrow towers). Finally, x tells you the amount of towers (or in multi-A numbers the expansion factor) of the particular function level. For example, a 2 in the x position would yield two towers. 

The Letters

Level 5: Alpha Notation which builds Conway Towers

Examples: 3AAA3, 4AAAA4, 5AAAAA5

Level 6: Beta Notation which builds Alpha Towers

Examples: 3BBB3, 4BBBB4, etc

Level 7: Gamma Notation (3GGG3)

Level 8: Delta Notation (3DDD3)

Level 9: Epsilon Notation (3EEE3)

Level 10: Zeta Notation (3ZZZ3)

Level 11: Eta Notation (3HHH3)

Level 12: Theta Notation (3-0-0-0-3)

Level 13: Iota Notation (3III3)

Level 14: Kappa Notation (3KKK3)

Level 15: Lambda Notation (3LLL3)

Level 16: Mu Notation (3MMM3)

Level 17: Nu Notation (3NNN3)

Level 18: Ksi (Xi) Notation (3XXX3)

Level 19: Omicron Notation (3OOO3)

Level 20: Pi Notation (3PPP3)

Level 21: Rho Notation (3RRR3)

Level 22: Sigma Notation (3SSS3)

Level 23: Tau Notation (3TTT3)

Level 24: Upsilon Notation (3UUU3)

Level 25: Phi Notation (3/0/0/0/3

Level 26: Chi Notation (3CCC3)

Level 27: Psi Notation (3YYY3)

Level 28: Omega Notation (3WWW3)


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