# Category:Partial Orderings

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This category contains results about Partial Orderings.

Definitions specific to this category can be found in Definitions/Partial Orderings.

Let $\struct {S, \preceq}$ be an ordered set.

Then the ordering $\preceq$ is a **partial ordering** on $S$ if and only if $\preceq$ is not connected.

That is, if and only if $\struct {S, \preceq}$ has at least one pair which is non-comparable:

- $\exists x, y \in S: x \npreceq y \land y \npreceq x$

## Subcategories

This category has only the following subcategory.

### E

## Pages in category "Partial Orderings"

The following 2 pages are in this category, out of 2 total.