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# Def/Partition

Definition of Partition: Suppose that $X$ is a set. A partition of $X$ is a set $I$ of subsets of $X$ (in other words, an element $I \in P(P(X))$, which satisfies the following property:

• For all $x \in X$, there exists a unique $i \in I$, such that $x \in i$.

A partition "breaks up" a set $X$ into disjoint pieces.

## Logical Connections

This definition logically relies on the following definitions and statements:

The following statements and definitions logically rely on the material of this page: Def/Cycle type, Def/Equivalence class, and State/Zolotarevs lemma

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