In the comments of the answer the author says they have a 4 and a 9 year old: "Bill, despite your emphatic comments, I know for a fact that counting into the o

In the comments of the answer the author says they have a 4 and a 9 year old: "Bill, despite your emphatic comments, I know for a fact that counting into the ordinals is something that children can easily learn. I have two young children (ages 4 and 9), who are happy to discuss ℵα for small ordinals α---although my daughter's pronunciation sounds more like Olive0, Olive1---and my son can count up to small countably infinite ordinals. The pattern below ωω is not difficult to grasp. Below ω2, it is rather like counting to 100, since the numbers have the form ω⋅n+k, essentially two digits"