Rational Numbers are Well-Orderable/Proof 1

Theorem

The set $\Q$ of rational numbers is well-orderable.


Proof

From Rational Numbers are Countably Infinite, $\Q$ is a countable set.

The result follows from Countable Set is Well-Orderable.

$\blacksquare$


Sources

  • 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $4$: Superinduction, Well Ordering and Choice: Part $\text I$ -- Superinduction and Well Ordering: $\S 1$ Introduction to well ordering: Discussion
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