Partition

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math

For a set \( A \) a [see page 21, partition] is a set of disjoint subsets of \( A \), \( A_i \forall i \in I \) 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].