# Definition:Chain (Order Theory)/Subset Relation

This page is about Chain of Sets in the context of Order Theory. For other uses, see Chain.

## Definition

Let $S$ be a set.

Let $\powerset S$ be its power set.

Let $N \subseteq \powerset S$ be a subset of $\powerset S$.

Then $N$ is a chain (of sets) if and only if:

$\forall X, Y \in N: X \subseteq Y$ or $Y \subseteq X$

## Also known as

A chain (of sets) is also known as a nest, particularly in the wider context of class theory.

## Also see

• Results about chains can be found here.