Definition:Trivial Partition

From ProofWiki
Jump to navigation Jump to search

Definition

Let $S$ be a set such that $S \ne \varnothing$.

There are two partitions on $S$ which are referred to as the trivial partitions on $S$:


Singleton Partition

The singleton partition on $S$ is defined as:

$\mathcal P = \left\{{S}\right\}$

That is, it is a partition with only one component.


Partition of Singletons

The partition of singletons on $S$ is defined as:

$\mathcal P = \set {\set x: x \in S}$

That is, it is a partition such that every component is a singleton.