User blog:Nedherman1/My Factorial vs HAN!!

(I Don't speak English)

In my last post, I demonstrated a very powerful factorial, but weaker than HAN and said that I would try to create a more powerful factorial than HAN and I believe I did!

Let's start by demonstrating how it works (Your basic idea):

'''[m; n] ^! = n ^ ... ^ n with n ^ ... ^ n arrows with n ^ ... ^ n arrows .                         . (repeated by m times) .          with n ^ ... ^ n arrows with n ^ ... ^ n arrows .                         . (repeats by (m-1) times) .                        ...          with n ^ ... ^ n arrows (repeats 1 time) with (n-1) ^ ... ^ n arrows with (n-1) ^ ... ^ n arrows .                         . (repeats by m times) .    with (n-1) ^ ... ^ n arrows with (n-1) ^ ... ^ n arrows .                         . (is repeated for (m-1) times) .                        ...             with 1 ^ n arrows (repeats 1 time)'''

The first time the "m" has been reduced to 1, when it reaches 1, on it is reduced by 1 and the process repeats itself back to normal and when it reaches 1 again the (n-1) is reduced by 1 and again the process returns.

                    

We can add another entry like:

'''[a; b; c]^! = [[a; b]; c]^! = [[a; b]^!; c]^!'''

we can add "n" inputs

'''However, this is still very "weak", we can make it stronger: (a-1)                           (a-1) [m; n] ^! = [m; n] ^          ! ^ ... ^ [m; n] ^       ! (a-1)                      (a-1) with [m; n]^     ! ^ ... ^ [m; n]^       ! arrows .                              (a-1) . (repeats ([m; n] ^       !) times) . '''

'''                                  (a-1)                       (a-1) with [m; n]^       ! ^ ... ^ [m; n]^       ! arrows'''

                                              ...

and this continues in the same way that has already been explained ''' It is important to say that the rule [m; n]^(with "a" arrows) ! only applies when a> 1, since a = 1 has already been shown how it is done. '''