Every set admits a well-ordering. Equivalent to AC; Zermelo's 1904 proof spurred foundational debate and motivated ZFC.
Well-ordering theorem
Related concepts
- Axiom of choice (AC)
- Ordinal number
- Dedekind cut & completeness
- Zorn's lemma (equivalent to AC)
- Ordinal analysis + consistency strength
- Haag's theorem: continuum-many unitarily inequivalent CCR representations (quantum)
- Bright soliton in anomalous-dispersion fibre: A(z,t) = √P_0 sech(t/T_0) exp(iγP_0 z/2)
- IUPAC lowest-locant tiebreak framework: first-point-of-difference rule for locant-set comparison (P-14.5.2)
- Gibson assembly