After the first course on real analysis, you might have realised that much of the richness of the set of all real numbers and its associated contexts are attributed to the completeness axiom of real numbers. This fundamental property underpins key results like the Archimedean property, the Bolzano-Weierstrass theorem, the Cantor’s intersection theorem, and the convergence of Cauchy sequences, amongst others. This property also distinguished the real numbers from the rationals in the axiomatic development.