Editing Partition of a set (section)

== Examples ==
*The empty set <math>\emptyset</math> has exactly one partition, namely <math>\emptyset</math>. (Note: this is the partition, not a member of the partition.)
*For any non-empty set ''X'', ''P'' = {{mset| ''X'' }} is a partition of ''X'', called the '''trivial partition'''.
**Particularly, every [[singleton set]] {''x''} has exactly one partition, namely {{mset| {{mset|''x''}} }}.
*For any non-empty [[proper subset]] ''A'' of a set ''U'', the set ''A'' together with its [[complement (set theory)|complement]] form a partition of ''U'', namely, {{mset| ''A'', ''U'' &setminus; ''A'' }}.
*The set {{mset|1, 2, 3}} has these five partitions (one partition per item):
** {{mset| {1}, {2}, {3} }}, sometimes written 1 | 2 | 3.
** {{mset| {1, 2}, {3} }}, or 1 2 | 3.
** {{mset| {1, 3}, {2} }}, or 1 3 | 2.
** {{mset| {1}, {2, 3} }}, or 1 | 2 3.
** {{mset| {1, 2, 3} }}, or 123 (in contexts where there will be no confusion with the number).
*The following are not partitions of {{mset|1, 2, 3}}:
** {{mset| {}, {1, 3}, {2} }} is not a partition (of any set) because one of its elements is the [[empty set]].
** {{mset| {1, 2}, {2, 3} }} is not a partition (of any set) because the element 2 is contained in more than one block.
** {{mset| {1}, {2} }} is not a partition of {{mset|1, 2, 3}} because none of its blocks contains 3; however, it is a partition of {{mset|1, 2}}.