06/07/2013, 09:03 PM
I realized this is a more efficient way of talking about hyper operators. I will still talk about those \( I \) sets, but I think it is a better approach to already have an analytic expression. It came to me in a stroke of luck when I was thinking about fractional derivatives.
The goal is to have \( f(s) = \frac{1}{x[s]y} \) for all \( x,y \in \mathbb{N} \) analytic and entire. The proof of recursion then only revolves around when the output is a natural number. So we only prove for a discrete set of reals.
The goal is to have \( f(s) = \frac{1}{x[s]y} \) for all \( x,y \in \mathbb{N} \) analytic and entire. The proof of recursion then only revolves around when the output is a natural number. So we only prove for a discrete set of reals.
