Disjoined units

In Mathématiques, two Ensemble S are known as disjoined if they do not have a element S joint. For example, {1, 2,3} and {4, 5,6} are 2 disjoined units.

Explanation

In a formal way, 2 units has and B is disjoined if them intersection is the Empty set, i.e. if

$A \ course B = \ varnothing. \,$

This definition extend to a collection from units. A collection of disjoined units two to two or mutually disjoins if any couple of 2 whole of this collection are disjoined.

Formally, either I a Together indexed, and for each I in I , or has _I a unit. then the family of units { has _I: I X I } is mutually disjoined so for any couple ( I , J ) in I × with I ≠ J ,

$A_i \ course A_j = \ varnothing. \,$

For example, the family {{1}, {2}, {3},…} is mutually disjoined. If { has _I} is a family mutually dijointe, then the intersection of all its units is empty:

$\ bigcap_ {I \ in I} A_i = \ varnothing. \,$

However, reciprocal is false: the intersection of the family is empty, but this family of is not mutually disjoined.

A partition X is a family of nonempty subsets { has _I: I ∈ I } of X such as { has _I} is mutually disjoined

$\ bigcup_ {I \ in I} A_i = X. \,$

Disjoined units

Explanation

See also