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Suppose I'm dividing some region $\Theta \in \mathbb{R}^n$ into subregions $\theta_i, i=1,2,3$ such that $\theta_i \cap \theta_j = \varnothing, i\ne j$ and $\bigcup_i \theta_i = \Theta$. I might say (perhaps loosely, even technically incorrectly) that I am partitioning the region $\Theta$.

Thus, a "partition" would be a particular configuration of $\{\theta_1,\theta_2,\theta_3\}$ that satisfies the aforementioned conditions. But what would an element of a partition be referred to as?

Since I am partitioning a "region", it makes sense to say that I am partitioning a region into "subregions", but at a higher level, what is a correct term for an element of a partition?

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Your definition of partition is the standard one: en.wikipedia.org/wiki/Partition_of_a_set. –  lhf May 14 '13 at 19:27
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up vote 5 down vote accepted

The terms cells, or classes, or blocks, even parts of a partition are often used to describe the "sub-regions" of a given partition, depending on the nature and/or context of the partition.

See for example, Partition of a Set.

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Would "cell" or "class" or "block" be more appropriate in the type of partition I described? –  synaptik May 14 '13 at 19:27
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I would say "cell", or "block" in your example. "Class" is used particularly when referring to the partition of a set determined by an equivalence relation: elements in the same "equivalence class" are related by the relation. –  amWhy May 14 '13 at 19:29
    
@amWhy: Nice to feel like you helped! +1 –  Amzoti May 15 '13 at 0:36
    
I just remember my own first encounter with the notion of a partition, and I kept confusing "partition" with one of it's classes/cells: So, e.g., I wanted to say "partition of even integers union partition of odd integers = integers"...For lack of a handy term to call one of the "subdivisions" created by a partition. –  amWhy May 15 '13 at 0:38
    
What about "coset"? Is that ever used for elements of an abstract partition, or is it only used for groups? –  bof Feb 18 at 21:14
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I have usually seen them referred to as parts or blocks of the partition. Partition of a Set

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