Tetration and p-adic

[Ember Edison]

But, I fully believe that for natural numbers, Marco has shown that \(^\infty a\) for \(a \in \mathbb{N}\) is always in \(\mathbb{Q}_p\)--for every prime. And it is never irrational.

I think irrationality will happen for \(^N a\) and \(\mathbb{N}\); and \(N\)'s relation to the prime \(p\). But, these are still in \(\mathbb{Q}_p\). And I believe that Marco's result; if not proves this result, casts a wide net of results in which \(^\infty a \in \mathbb{Q}_p\). Rather than being irrational, in \(^\infty a \in \mathbb{R}_p / \mathbb{Q}_p\)...... The digits where we take Rational numbers, and tend to infinity, we see a repeatable pattern. Which looks like Marco's modular stuff. And studying that; talks about lists of digits, their repeating patterns, under tetration, under the norm where growth shrinks, and shrinking grows....

Wow, it does feel like becoming an eyewitness to a new frontier.