There is a way of mapping different ordinal numbers which are less than some large countable ordinal (idr how high up it goes. I suspect it isn’t well defined a

There is a way of mapping different ordinal numbers which are less than some large countable ordinal (idr how high up it goes. I suspect it isn’t well defined at least past the church kleene ordinal, but I think it is much before that, but also I could be totally wrong) to different functions from integers to integers which increase at different rates. These methods include the Hardy hierarchy, and the fast growing hierarchy. (But regarding all infinities being equal, that’s just incorrect, sorry.)