Fractional iteration of x^2+1 at infinity and fractional iteration of exp

[Catullus]

exp(x) + x has a " true " fixpoint at oo.

Exp(∞) may be a larger infinity.

Hmmmmm, you'd have to qualify that using some kind of framework. No idea what that would be. You could use something like Hardy spaces, and refer to \(1/\exp(\infty)\) in the right half plane as smaller than \(1/\infty\) in the right half plane. But then, you'd have to qualify how you mean this. Typically we're not referring to growth hierarchies. And they don't apply to Tommy's comment.

Exp(\( \aleph_0 \)) = ℶ1.