A basic description of a Set is a well-determined collection of objects, called members (or elements). In Set theory, sets are given axiomatically such that their existence and basic properties follow. The axioms of set theory imply that all mathematical objects (such as the set of Whole numbers, or Real numbers) may be construed as a set. Consequently, Set Theory is used to formalize mathematical notions and arguments to the extent that it forms a standard foundation for mathematics. Additionally, if one studied Foundations, one would also learn that Gödel employed Set Theory to the set of natural numbers (an arithmetic set) in order prove his incompleteness theorem.
Rich in history and development, much of the rigorous formalizations of set theory were laid out by Georg Cantor in the 1870s. Additional contributions have been made by Zermelo, Fraenkel & Von Neumann form the foundation of the standard axiom system of set theory (known as Zermelo-Fraenkel + Axiom of Choice, or ZFC). The axioms of Set Theory can easily lose any undergraduate mathematics student. Fortunately Homework Help has an array of logicians and math specialists ready to help you navigate your assignments. Trust the experts at Homework Help USA and get a quote now.