User blog:MachineGunSuper/MGS' Hyper Diagonalizing Function (MHDF)

This is a function that I have used in one of my listament functions.

By itself it's clearly not fast growing, but with the help of other functions it can dominate computable functions.

It's a form of diagonalization.

A = 1,2,3,4,.....      3,4,5,6,.....       5,6,7,8,.....       7,8,9,10,.... MHDF (A,b) = b-th element from diagonalizing in A Eg: MHDF (A,3) = 7

The reason why this is able to dominate all computable functions is because the definition of this is a list of numbers on which you can diagonalize. But that list can also contain other elements

Rule: Below a number comes that number+2, as you can see on A

Now, for the "cooler" part We can replace each element with say, a number in the graham function.

B = g1,g2,g3,g4,.....      g3,g4,g5,g6,.....       g5,g6,g7,g8,.....       g7,g8,g9,g10,....

MHDF (B,3) = g7 = 3↑g63 We used a mere 3 and got g7

'''Additional rule that can make writing harder: You may have noticed that in order to "tell" someone a number you must show them the list too. But you can do this: We can write MHDF (B,3) as MHDF (a list with numbers from graham function,3). That way you won't have to always draw that list.'''