User blog comment:Edwin Shade/Understanding The Infinite/@comment-32213734-20171110205605/@comment-5529393-20171110211048

Each version has some claim on being "simpler". I would agree that, for successor α, it is simpler to just take the fixed point of the previous function. However, that means that Rule 2 as a whole must be subdivided into two parts, one for successor α and one for limit α. On the other hand, Edwin's version just has the limit rule, so that is clearly simpler as a whole. But, separating out the successor version might make things more clear to the reader.