User blog:MachineGunSuper/My Page

I am fascinated by factorial numbers and how you can modify them to make way stronger functions. I have defined many numbers ending in the suffix -bulls. Because why not?

I have made many things similar to it such as:

The Listaments: All factorization (with any value of n) of the total combinations possible to arrange the result of a powertower of numbers within a specific range, starting with the smallest and ending with the biggest. However, the first numbers must not be 0,1. They can be written like this: '''^^''' =  x!(x!+1) (x!+2) (x!+3) ...... (y!-2) (y!-1) y!     

These listaments can define an infinite amout of functions, wich have their growth rate increase everytime you create a brand new one, wich means that creating a big but finite number of functions, you will get one that dominates all computable functions. The slowest possible function that follows this rule is simply called The Listament Function and it looks something like this:

'Listt! (n)'

'Listt! (500) = 2!3! 4! 5! . . . 499! 500!      '

Next up after this comes The Free Listament Function . It is defined as repeating 'Listt! (n)s

'Listt!! [n] = Listt! ( Listt! (Listt! (......... (Listt! (n))))....))), with Listt! (n) "Listt!" 's '

'Listt!! [3] = Listt! (Listt! (Listt! (..... ( Listt! (3)))....))), with 64 "Listt!"'s (because Listt! (3) = 64)'

'Listt!! [3] = Listt! (........ (Listt! (Listt! (64))..), with 63 "Listt!" 's'

'Listt!! [3] = Listt! (........... (Listt! (62 PT (1.107687858235 * 1091)))...)), with 62 "Listt!"'s'

While it would take more than the universe has lived years to calculate this number by hand, but you can tell that this function grows quicly since:

- The first number was a merely 64

- The second number was a big 62 PT (1.107687858235 * 1091)

- You can guess how big the resulting number might be after doing this huge jump 62 more times.

Call the result of '''Listt!! [3] = X'''

The next fastest growing function that follows the rules is the Busy Listament Function (sorry for unoriginal name). It is defined as repeating '''Listt!! [n] '''functions.

'Listt!!! {n} = Listt!! [ Listt!! [ Listt!! [......... [ Listt!! [n]]]]....]]]], with Listt!! [n] "Listt!!" 's '

'Listt!!! {3} = Listt!! [Listt!! ....... [ Listt!! [3]]]...]]]], with "X" (check what I said above) "Listt!! 's "'

'Listt!!! {3} = Listt!! [......... [Listt!! [X]]].....]]]], with X-1 Listt!!'s .'

Call the result of '''Listt!!! {3} = Y'''

The next function that follows the rules is the Very Busy Listament Function , wich is defined as repeating

'''Listt!!! {n} '''functions.

'Listt!!! = Listt!!! {Listt!!! {Listt!!! {......... {Listt!!! {n}}...}}}, with Listt!!! {n} "Listt!!!" 's '

'Listt!!! = Listt!!! {Listt!!! { ........... { Listt!!! {3}}}}....}}}}, with Y Listt!!!'s'

'Listt!!! = Listt!!! {...... {Listt!!! {Y}}.....}}}, with Y -1 Listt!!!'s'

'''Now of course, Listt!!! is not the biggest number out there, but it is basically impossible to calculate.'''

The next function is Not Free Listament Function , wich is defined as repeating '''Listt!!! '''functions.

'Listt! {[n]} = Listt!!! {{ Listt!!! {{Listt!!! {{........ {{Listt!!!}....}}}, where "Listt!!! {{" repeats  Listt!!! times.'

'Listt! {[3]} = Listt!!! {{Listt!!! {{Listt!!! {{....... {{Listt!!!{3}}}}....}}}}, with Listt!!! "Listt!!! {{"'s.'