Editing Cofiniteness (section)

{{short description|Being a subset whose complement is a finite set}}
{{Distinguish|cofinality}}
In [[mathematics]], a '''cofinite''' [[subset]] of a set <math>X</math> is a subset <math>A</math> whose [[Complement (set theory)|complement]] in <math>X</math> is a [[finite set]]. In other words, <math>A</math> contains all but finitely many elements of <math>X.</math> If the complement is not finite, but is countable, then one says the set is [[cocountable]].

These arise naturally when generalizing structures on finite sets to infinite sets, particularly on infinite products, as in the [[#Product topology|product topology]] or [[#Direct sum|direct sum]]. 

This use of the prefix "'''{{em|co}}'''" to describe a property possessed by a set's [[Complement (set theory)|'''{{em|co}}'''mplement]] is consistent with its use in other terms such as "[[Comeagre set|'''{{em|co}}'''meagre set]]".