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Set Theory is the true study of infinity. This alone assures the subject of a place prominent in human culture. But even more,
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Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects.Although any type of object can be collected into a
set,
set theory is applied most often to objects that are relevant to mathematics.
Set theory is the mathematical
theory of well-determined collections, called sets, of objects that are called members, or elements, of the
set.Pure
set theory deals exclusively with sets, so the only sets under consideration are those whose members are also sets. 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 Zermelo–Fraenkel
set theory, the notion of
class is informal, whereas other
set theories, such as von ...
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Set theory, branch of mathematics that deals with the properties of well-defined collections of objects, which may or may not be of a mathematical nature, such as numbers or functions.The
theory is less valuable in direct application to ordinary experience than as a basis for precise and adaptable terminology for the definition of complex and sophisticated mathematical concepts.
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von Neumann-Bernays-Gödel set theory (abbreviated "NBG") is a version of
set theory which was designed to give the same results as Zermelo-Fraenkel
set theory, but in a more logically elegant fashion. It can be viewed as a conservative extension of Zermelo-Fraenkel
set theory in the sense that a statement about sets is provable in NBG if and only if it is provable in Zermelo-Fraenkel
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