(related to Proposition: Order Relation for Rational Numbers is Strict Total)

In order to avoid complicated distinctions of cases, we can without loss of generality assume the integers $a,b,c,d,e,f\in Z$ to be all positive integers. We first show the trichotomy of the order relation "$<$" for rational numbers \(\frac ab,\frac cd, \in\mathbb Q\):

We now show the transitivity.

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