User blog:ANDY3556/Andrew's Improved A-Notation

I have decided to revise my A notation. If you're not familiar with the rules of the original, click here. This notation was meant to be an improvement, so let's get started.

\(A(x)\)=x x-ated to itself x times. Think of an x-ational power tower where all the numbers are x: that tower would go on for x terms.

\(A(x, y)\)=\(A(A(A(...A(x)))))\) where the nesting happens y times.

\(A(x, y, z)\)=\(A(A(A(...A(x, y))))\) where the nesting happens z times.

Of course, \(A(x, y, z, w)\)=\(A(A(A(A(...A(x, y, z))))\) where the recursion happens w times...

and in general, if you have an n-entry A, then its value is a constant "nesting" of A's [where the last layer is n-1 entry A] where the nesting happens x times, where x is the last entry.

\(A\#\x(y)\) is x-entry A where every term is y.

If x and y are the same number, use \(A&x\).

\(A*(x)\)=\(A(A(A(...A(x, x)))))\) where the nesting happens \(A(x, x)\) times.

\(A*(x, y)=A(A(A(A(A(...A(x, y)))))\) where the nesting happens \(A(x, y)\) times.

\(A*(x, y, z)=A(A(A(A(...A(x, y, z))))\) where the nesting happens \(A(x, y, z)\) times, and so on.

\(A2(x)\) is \(A(x)\) A(x)-ated to \(A(A(A(A(A(...A(x)))))\) where the nesting happens \(A(x)\) times.

\(A3(x)\) is \(A2(x)\) A2(x)-ated to \(A(A(A(A(A(...A2(x))))))\) where the nesting happens \(A2(x)\) times and so on.

The \(A\@\x(y)\) operator basically does the \(A\#\x(y)\) operator but nests it inside a chain of A's \(A\#\x(y)\) times.

What do you guys think about this new improved notation?