Definition:Partition

From CS2800 wiki
Definition: Partition
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:
  1. 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].
  2. 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:

Partition.svg