Assertion: class | /r/HasProperty | proper
Facets:
value: in many formal systems
type: LOCATION
Source sentences:
text: One way to prove that a class is proper is to place it in bijection with the class of all ordinal numbers.
text: For instance, the class of all ordinal numbers, and the class of all sets, are proper classes in many formal systems.
text: A class that is not a set (informally in Zermelo–Fraenkel) is called a proper class, and a class that is a set is sometimes called a small class.
text: For example, Russell's paradox suggests a proof that the class of all sets which do not contain themselves is proper, and the Burali-Forti paradox suggests that the class of all ordinal numbers is proper.