User blog:Xtrasnack/Moser Array Notation

Moser arrays
I was looking at Susan Stepney's general Moser notation, and thought it looked somewhat like an array. Here is my Notation: (@ represents the rest of the array)

[n] = n [n,1 @] = [nn  @] [a,b @] = [a,b-1,b-1,b-1,b-1... @] with a b-1s

I changed the lowest shape from 3 to 1 for simplicity. This by itself is not any more powerful than Moser notation. But, as in numbers like Moser, They are solved in reverse.

 = n <@ a,b> = <@ [a,b]> Solve the inner array first.

Here is the next operator, it is the Moser equivilant of "array of".

a%b =  with a bs

Next is the $ operator.

a$(1,1)b = b%b%b%b%b... with a %s, solved frontwards. a$(b,1)c = a$(b-1,(a$(b-1,(a$(b-1,(a$(b-1... $(b-1,c)c))c))c))c))c... with a $s a$(b,c)d  = d$(b-1,c)d$(b-1,c)d$(b-1,c)d... with a $s

The next is the Snack function

Snack(n) = n$(n,n)n

Here is the next level of this:

Snack{1}(n) = Snack(n) Snack{a}(b) = Snack{a-1}(Snack{a-1}(Snack{a-1}(...(b))))... with b Snacks

Here is another value:

Snack{a,1}(b) = Snack{a}(b) Snack{a,b}(c) = Snack{ Snack{ Snack{ Snack{... Snack{a,b-1}(c),b-1}(c),b-1}(c),b-1}... (c) with c Snacks

You can add on as many values as you want of this. But herre is the diagonalization of this:

a#b = a%b a##b = Snack{b,b,b,b...}(b) with a bs.

You can continue this, but just replace % in the previous definitions with ##.

a###b a####b

...

Now we can write this /n Here is the last function to define:

Supersnack(n) = n/n/n/n/...n/n ...