examples of ring of sets
Let be a non-empty set containing an element . Let be the family of subsets of containing . Then is a ring of sets, but not a field of sets, since , but .
A simple example of a ring of sets is the subset of . That this is a ring of sets follows from the observations that and . Note that it is not a field of sets because the complement of , which is , does not belong to the ring.
Another example involves an infinite set. Let be an infinite set. Let be the collection of finite subsets of . Since the union and the intersection of two finite set are finite sets, is a ring of sets. However, it is not a field of sets, because the complement of a finite subset of is infinite, and thus not a member of .
|Title||examples of ring of sets|
|Date of creation||2013-03-22 15:47:52|
|Last modified on||2013-03-22 15:47:52|
|Last modified by||rspuzio (6075)|