Subclass (set Theory)
In set theory and its applications throughout mathematics, a subclass is a class contained in some other class in the same way that a subset is a set contained in some other set. That is, given classes ''A'' and ''B'', ''A'' is a subclass of ''B'' if and only if every member of ''A'' is also a member of ''B''. If ''A'' and ''B'' are sets, then of course ''A'' is also a subset of ''B''. In fact, when using a definition of classes that requires them to be first-order definable, it is enough that ''B'' be a set; the axiom of specification essentially says that ''A'' must then also be a set. As with subsets, the empty set In mathematics, the empty set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. Some axiomatic set theories ensure that the empty set exists by including an axiom of empty set, while in oth ... is a subclass of every class, and any class is a subclass of itself. But additionally, every class is a subclass ...
[...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]