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In set theory and its applications throughout mathematics,
a class is a collection of sets (or sometimes other mathematical objects) that
can be unambiguously defined by a property that all its members share.

The precise definition of "class" depends on foundational context.
In work on Zermeloโโ‚ฌโ€œFraenkel set theory, the notion of class is informal,
whereas other set theories, such as von Neumannโโ‚ฌโ€œBernaysโโ‚ฌโ€œGรถdel set theory,
axiomatize the notion of "proper class",
e.g., as entities that are not members of another entity.


Many discussions of "classes" in the 19th century and earlier are really referring to sets,
or perhaps rather take place without considering that certain classes can fail to be sets.