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 $\mathcal R \subseteq S \times S$ be a relation on a set $S$.

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

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

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

$\forall x, y \in S: x \mathop {\mathcal R} y \lor y \mathop {\mathcal R} x$

Subcategories

This category has the following 7 subcategories, out of 7 total.

G

L

M

O

T

W

Pages in category "Total Orderings"

The following 55 pages are in this category, out of 55 total.