Category:Total Orderings

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This category contains results about Total Orderings.
Definitions specific to this category can be found in Definitions/Total Orderings.

Let $\RR \subseteq S \times S$ be a relation on a set $S$.

$\RR$ is a total ordering on $S$ if and only if:

$(1): \quad \RR$ is an ordering on $S$
$(2): \quad \RR$ is connected

That is, $\RR$ is an ordering with no non-comparable pairs:

$\forall x, y \in S: x \mathop \RR y \lor y \mathop \RR x$

Pages in category "Total Orderings"

The following 72 pages are in this category, out of 72 total.