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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. One may also call this "inclusion of classes". 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. [1]
symbolic of realization (subclass) _____ (superclass) Dual to generalization is the specialization relationship. Other terms for a (specialized) subclass of a more general superclass include subtype, derived class, derived type, inheriting class, inheriting type, child, and child class.
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This usage dates from a historical period where classes and sets were not distinguished as they are in modern set-theoretic terminology. [1] Many discussions of "classes" in the 19th century and earlier are really referring to sets, or rather perhaps take place without considering that certain classes can fail to be sets.
The Zentralblatt MATH page on the Mathematics Subject Classification. MSC2020 can be seen here. Mathematics Subject Classification 2010 – the site where the MSC2010 revision was carried out publicly in an MSCwiki. A view of the whole scheme and the changes made from MSC2000, as well as PDF files of the MSC and ancillary documents are there.
In mathematics, a set A is a subset of a set B if all elements of A are also elements of B; B is then a superset of A. It is possible for A and B to be equal; if they are unequal, then A is a proper subset of B. The relationship of one set being a subset of another is called inclusion (or sometimes containment).
The subclass re-uses all of the functionality of the base class with the exception of the operation that transforms a number into its square, replacing it with an operation that transforms a number into its square and cube respectively. The subclasses therefore compute the sum of the squares/cubes between two integers. Below is an example of ...
Category theory is a branch of mathematics that seeks to generalize all of mathematics in terms of categories, independent of what their objects and arrows represent. Virtually every branch of modern mathematics can be described in terms of categories, and doing so often reveals deep insights and similarities between seemingly different areas ...