User blog:Durvensonisback/Durvenson Notation

This is a function sort of mimicking the nature of uncomputable numbers. I have no clue as to the growth rate of this notation relative to the other function inputted into it. fr([a,b,c,d...]) takes a linear array of numbers. Here is how to solve for a given equation:

1. Repeat these steps until you only have one number with just 2s before it, and just 2s after it.

1.1. Repeat the steps below until you end up with empty spots that are not after the last entry in the z, and are not before the 1st entry in z.

1.12. Take the current set, and call it x. Take this current set, reverse it, and call it y.

1.13. Make a third array called z. Take the 1st member of y, and in this new array, put x at that posistion of the array. If you have to put a member of x where a member of x already exists, then take the currently occupied member of x, call it a, and take the member that would have gone in that same spot, and call it b. Replace the spot where both are put in with f(a,b) (f is specifed before the r).

1.2. If there are empty spots that are not after the last entry in the z, and are not before the 1st entry in z, replace them with 2s.

2. The 2s can be removed, and the only number in the array will be the output.

fd(a,b) is the smallest number such that it uses fr[x,y,z...], where the [x,y,z...] uses only integers from 2 to a, and only has 1 to b members.

A extension of this notation exists, which is called Durvenson Notation Hireachy.

It is defined as so:

D_0([a],[b]) = (a*b)d([a],[b])

D_n([a],[b]) = D_n(a,b)(D_n(a,b)(D_n(a,b)(...[a]...))) [b] copies

D_w([a],[b]) = D_[a]([a],[b])

D_w+1([a],[b]) = D_w(a,b)( D_w(a,b)( D_w(a,b)(...[a]...))) [b] copies

D_2w([a],[b]) = D_w+[a]([a],[b])

D_2w+1([a],[b]) = D_2w(a,b)(D_2w(a,b)(D_2w(a,b)(...[a]...))) [b] copies

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