Ordinal function: Difference between revisions

Technically speaking and within [[ZFCZF]], since [[Burali–Forti paradox|ordinals don't form a set]], one can't formally talk about functions \(f:\text{On}\to\text{On}\). However, replacing \(\text{On}\) with the set of ordinals below a large enough ordinal, such as an [[inaccessible ordinal]] or even an [[uncountable]] or [[principal]] ordinal, depending on context, is almost always enough to formally recover any results on them. As such, we still refer to them as functions from ordinals to ordinals in the wiki.