Partition

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math

For a set $A$ a [see page 21, partition] is a set of disjoint subsets of $A$, $A_i\mathrm{\forall }i\in I$ where the intersection of all the elements of the partition gives back $A$. That is $\bigcup _{i\in I}{A}_i=A$.

We define a specific element of the partition (for example $A_0$) as a block.

Partition Refinement

A partition where every block is a subset of a block of the one being [see page 21, refined].