A
collection of
subsets [math]A_1, A_2, \dots, A_n
[/math] of a
set [math]A
[/math] form a
partition of
[math]A
[/math] if:
- The [math]\href{/cs2800/wiki/index.php/Sequence_notation}{A_i}
[/math] cover [math]A
[/math], i.e. [math]A \href{/cs2800/wiki/index.php/Equality_(sets)}{=} A_1 \href{/cs2800/wiki/index.php/%E2%88%AA}{∪} A_2 \href{/cs2800/wiki/index.php/%E2%88%AA}{∪} \cdots \href{/cs2800/wiki/index.php/%E2%88%AA}{∪} A_n
[/math].
- The [math]A_i
[/math] are disjoint, i.e. [math]A_i \href{/cs2800/wiki/index.php/%E2%88%A9}{∩} A_j = \href{/cs2800/wiki/index.php/%E2%88%85}{∅}
[/math] unless [math]i = j
[/math].
The Venn diagram of a partition looks like this:
