Editing Enumeration (section)

===Listing===

When an enumeration is used in an [[sequence|ordered list]] context, we impose some sort of ordering structure requirement on the [[Index set (recursion theory)|index set]]. While we can make the requirements on the ordering quite lax in order to allow for great generality, the most natural and common prerequisite is that the index set be [[well-ordered]]. According to this characterization, an ordered enumeration is defined to be a surjection (an onto relationship) with a well-ordered domain. This definition is natural in the sense that a given well-ordering on the index set provides a unique way to list the next element given a partial enumeration.