Set theoryis the branch of mathematical logicthat studies sets, which 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. The language of set theory can be used in the definitions of nearly all mathematical objects. The modern study of set theory was initiated by Georg Cantorand Richard Dedekindin the 1870s. After the discovery of paradoxesin naive set theory, numerous axiom systemswere proposed in the early twentieth century, of which the Zermelo–Fraenkel axioms, with the axiom of choice, are the best-known. Set theory is commonly employed as a foundational system for mathematics, particularly in the form of Zermelo–Fraenkel set theorywith the axiom of choice. Beyond its foundational role, set theory is a branch of mathematicsin its own right, with an active research community. Contemporary research into set theory includes a diverse collection of topics, ranging from the structure of the real numberline to the study of the consistencyof large cardinals.
Posted on: Sun, 22 Sep 2013 06:11:32 +0000
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