Category:Examples of Orderings
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This category contains examples of Ordering/Definition 1.
$\RR$ is an ordering on $S$ if and only if $\RR$ satisfies the ordering axioms:
\((1)\) | $:$ | $\RR$ is reflexive | \(\ds \forall a \in S:\) | \(\ds a \mathrel \RR a \) | |||||
\((2)\) | $:$ | $\RR$ is transitive | \(\ds \forall a, b, c \in S:\) | \(\ds a \mathrel \RR b \land b \mathrel \RR c \implies a \mathrel \RR c \) | |||||
\((3)\) | $:$ | $\RR$ is antisymmetric | \(\ds \forall a, b \in S:\) | \(\ds a \mathrel \RR b \land b \mathrel \RR a \implies a = b \) |
Pages in category "Examples of Orderings"
The following 12 pages are in this category, out of 12 total.
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- Ordering on Natural Numbers is Compatible with Addition
- Ordering on Natural Numbers is Compatible with Addition/Corollary
- Ordering on Natural Numbers is Compatible with Multiplication
- Ordering on Natural Numbers is Compatible with Multiplication/Corollary
- Ordering/Examples
- Ordering/Examples/American Presidency
- Ordering/Examples/Example Ordering on Integers
- Ordering/Examples/Integer Difference on Reals
- Ordering/Examples/Monarchy