User blog comment:Elberos/Help?/@comment-35470197-20181219153612/@comment-35470197-20181220152239

@Rpakr

In both cases, the fixed point is much larger than the countable iteration.

@MGS

What definition of "uncountable iteration" are you considering? Unlike the countable iteration, it is quite ambiguous, because the usual transfinite composition (in category theory or homotopy theory) does not work well against functions with fixed points. Anyway, the fixed point is much larger than any "reasonable" formulation of "uncountable iteration with cofinality \(\aleph_1\)".