Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?

share|cite|improve this question
Your definition of partition is the standard one: – lhf May 14 '13 at 19:27
up vote 4 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.

share|cite|improve this answer
Would "cell" or "class" or "block" be more appropriate in the type of partition I described? – synaptik May 14 '13 at 19:27
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 '14 at 21:14

I have usually seen them referred to as parts or blocks of the partition. Partition of a Set

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.