---- > [!theorem] Theorem. ([[well-ordering theorem]]) > If $A$ is a set, there exists an [[strict order relation]] on $A$ that is [[well-ordered set|well-ordering]]. > \ > As a corollary, there exists an [[uncountably infinite|uncountable]] [[strict order relation|well-ordered set]]. > [!proof]- Proof. ([[well-ordering theorem]]) > Take a set theory class. ---- #### ----- #### References > [!backlink] > ```dataview TABLE rows.file.link as "Further Reading" FROM [[]] FLATTEN file.tags GROUP BY file.tags as Tag > [!frontlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM outgoing([[]]) > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ```