User blog:Mush9/Sebastian's number

My name's not Sebastian, it's just a great anonymous name ;P

Besides that, I decided on a proper notation, which shall lead up to the number, hopefully it's pretty big :P

{a} => {a,a,a,...}

When using {a}, it shall be treated as {a,a,a,...}, with a hash length equal to a.

{} => {0}

{a,b} => {a,b,a}

{a,b,c,d} => {a,b,c,d,c,b,a}

{a,b,c,d,e,f} => {a,b,c,d,e,f,e,d,c,b,a}

...

When the length of the hash is even, except 0, the last letter shall be removed, the hash shall be reversed, the last letter shall be readded, and the reversed hash shall be added.

{a,b,c,d,...} => a↑^(b↑^(c↑^(d↑^(...)d)c)b)a

Each integer above the first represents the number of up arrows used - in compliance with [].

A property of this is that - { {3} } = { {3,3,3} } = {Tritri} - in other words, a double hash of three becomes equal to: Tritri↑^(Tritri↑^(Tritri↑^(...)Tritri)Tritri)Tritri, where the repetance of Tritri is at least equal to Tritri times.

[a,0] => {}

[a,1] => {a}

[a,4] => { { { { a } } } }

'''[a,b] => { { { ... a,a,a,... ... } } }'''

To expand this notation further, arrays can be used, where hashes are overlapped exactly b times.

[a] = [a,a]

[a,b,c,...] => {a,b,c,...}

Remember, the array can be condensed, and unreasonable expansions are just treated as regular hashes.

This notation shall be known as Sebastian's notation, and Sebastian's number shall be known as:

'''[googolplex] => [googolplex, googolplex] => { { { ... googolplex,googolplex,googolplex,... ... } } }'''

''Out of interest, is anyone able to quantify that based on other large numbers? Is it larger than TREE(3) or Graham's number... or Utter Oblivion?''