Cascading Hyper Notation (CHN) is the 8th part of HN.

Rules

An expression is of the form H<n,A>, where n is the base and A is an array.

1. If there is no array, H<n> = n^n
2. If the array's first entry is 1, delete it.
3. If the array is a sequence array, decrease it by one, then nest the whole expression into the base n times.
4. If the array is a limit array, change the array into the nth member of it's FS.

Arrays

This part uses the same definitions as PCHN.

Define:

N*1 = N (N is an array)

N^1 = X, and N^1*A = N*A

N^A*(B-1)+N^A = X*B (where B is sequence array and A is any array)

The nth member of N^A*B's (where B is limit array) FS is N^A*FS(B,n)

N^(A-1)*N (where A is sequence ordinal) = N^A

The nth member of N^A's (where A is limit array) FS is N^FS(A,n)

Now, to compare arrays:

1. Look if the arrays have an X at the start. If array A does and array B doesn't, then A is bigger then B.

2. Else, look at the array after the first ^ for both arrays, and then, compare the two arrays that you just found, and that is your result, but if they are equal:

3. Look at the array after the * after the array after first ^ for both arrays, and then, compare the two arrays that you just found, and that is your result, but if they are equal:

4. Look at the array after the + after the array after the * after the array after the first ^ for both arrays, and then, compare the two arrays that you just found, and that is your result.