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References to 'completeness principle'
1. $0\ne 1$ as real numbers by mps
2. Archimedean property by Daume
3. axiomatic definition of the real numbers by matte
4. bounded complete by CWoo
5. every ordered field with the least upper bound property is isomorphic to $\mathbb{R}$, proof that by mps
6. every ordered field with the least upper bound property is isomorphic to the real numbers by archibal
7. linear continuum by azdbacks4234
8. proof of Heine-Borel theorem by stevecheng
9. real number by djao
10. uniformities on a set form a complete lattice by mps