If the collection of all ordinals were a set Ω, then Ω would be transitive and well-ordered by ∈, hence itself an ordinal, giving Ω ∈ Ω and contradicting foundation. Discovered by Cesare Burali-Forti in 1897 before ZFC; in ZFC it is…
If the collection of all ordinals were a set Ω, then Ω would be transitive and well-ordered by ∈, hence itself an ordinal, giving Ω ∈ Ω and contradicting foundation. Discovered by Cesare Burali-Forti in 1897 before ZFC; in ZFC it is…