Set Partition/Examples

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Examples of Set Partitions

Integers by Sign

Let $\Z$ denote the set of integers.

Let $\Z_{> 0}$ denote the set of strictly positive integers.

Let $\Z_{< 0}$ denote the set of strictly negative integers.

Let $\Z_0$ denote the singleton $\set 0$


Then $P = \set {\Z_{> 0}, \Z_{< 0}, \Z_0}$ forms a partition of $\Z$.


Partition into Singletons

Let $S$ be a set.

Consider the family of subsets $\family {\set x}_{x \mathop \in S}$ indexed by $S$ itself.

Then $\family {\set x}_{x \mathop \in S}$ is a partitioning of $S$ into singletons.

Its associated partition is:

$\set {\set x: x \in S}$