Well-Ordering Theorem
Jump to navigation
Jump to search
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.
The Well-Ordering Theorem was proved by Zermelos in 1904, and it states:
Every set can be well-ordered.
This result surprised mathematicians everywhere. The Well-Ordering Theorem is equivalent of the Axiom of Choice, and no well-ordering relation has ever been explicitly constructed for uncountable sets. Thus, the mathematicians who reject the Axiom of Choice also reject this theorem.