View source for Equivalences of Well-ordered Relation - Rhea

<h1>
Equivalences of Well-ordered Relation
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<h2>
Definitions
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<p>
<math>\langle A, R \rangle</math> is an totally ordered class iff
<ol>
<li>(R is a relation on A) <math>R\subseteq A\times A</math></li>
<li>(irreflexivity) <math>\forall x \in A\, \langle x,x \rangle \notin R</math></li>
<li>(transitivity) <math>\forall x,y,z \in A\, \langle x,y \rangle \in R \wedge \langle y,z \rangle \in R \rightarrow \langle x,z \rangle \in R</math></li>
<li>(trichotomy) <math>\forall x,y \in A\, \langle x,y \rangle \in R \vee \langle y,x \rangle \in R \vee x=y</math></li>
</ol>
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