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 "$ > $".
Table of Contents
Proofs: 1
Mentioned in:
Proofs: 1
Thank you to the contributors under CC BYSA 4.0!
 Github:
