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