Proposition: Order Relation for Rational Numbers is Strict Total
The order relation for rational numbers "$<$" defines a strict total order on the set $\mathbb Q$ of , i.e. for any rational numbers \(\frac ab,\frac cd,\frac ef\in\mathbb Q\), we have
- Only one of the following cases can be true: either \(\frac ab=\frac cd\), or \(\frac ab > \frac cd\), or \(\frac ab < \frac cd\) trichotomy).
- If $\frac ab < \frac cd$ and $\frac cd < \frac ef$, then $\frac ab < \frac ef$ transitivity).
- The same applies for the relation "$ > $".
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