# Category:Definitions/Well-Orderings

This category contains definitions related to Well-Orderings.
Related results can be found in Category:Well-Orderings.

The ordering $\preceq$ is a well-ordering on $S$ if and only if every non-empty subset of $S$ has a smallest element under $\preceq$:

$\forall T \subseteq S: \exists a \in T: \forall x \in T: a \preceq x$

## Subcategories

This category has only the following subcategory.

## Pages in category "Definitions/Well-Orderings"

The following 13 pages are in this category, out of 13 total.