Definition of Class (set theory)

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. Some classes are sets (for instance, the class of all integers that are even), but others are not (for instance, the class of all ordinal numbers or the class of all sets). A class that is not a set is called a proper class.