The History of Set Theory

Mathematicians have been using the set since the beginning of the subject. For example, the Greek mathematician defines a circle as the set of fixed points at a distance r from a fixed point P. However, the concept of 'infinite set' & limited 'to avoid the set of mathematicians and philosophers for centuries. For example, the Hindu mind is understood in their infinite Ishavasy-opanishad scripture text as follows: "Overall there. The whole being here. From the hole imanates whole. Get rid of the whole of the whole, what remains is still a Whole". Phythagoras (~ 585 -500 BC), a Greek mathematician, good and evil associated with the finite and infinite, respectively. Aristotle (384-322 BC) said, "infinity is not perfect, not yet finished and therefore, unthinkable, it's out of shape and confused. "Roman Emperor and philosopher Marcus Aqarchus (121-180 AD) said infinity is a fathomless gulf, where everything is gone" philosopher. British Thomas Hobbes (1588-1679) said, "When we say something is infinite, we signify only that we can not conceive ends and boundaries thing named".
Mathematicians work, as well as roads, rarely associated with unusal question: what numbers? However, attempts to answer this question it has driven a lot of work by the mathematician and philosopher at the foundations of mathematics during the last hundred years. Characterization of integers, rational and real numbers has become a classic problem of the center for the study of Weierstrass, Dedekind, Kronecker, Frege, Peano, Russell, Whitehead, Brouwer, and others. Researchers from the Georg Cantor around 1870 in a theory with infinite series and related topics of analysis provides a new direction for the development of set theory. Cantor, who is usually regarded as the founder of set theory as a mathematical discipline, led by his work into consideration the set of infinite or arbitrary character classes.
However, Cantor's results are not immediately accepted by his contemporaries. Also, it was found that the definition of the set leads to logical contradictions and paradoxes. The most famous among these is given in 1918 by Bertrand Russell (1872-1970), now known as Russell's paradox.
In an effort to resolve this paradox, mathematicians first reaction is to 'axiomatize' Cantor's intuitive set theory. Axiomatization is as follows: starting with a clear set of statements called axioms, the truth is assumed, one can deduce all the remaining propositions of the theory of logical axioms using the inference axioms. Russell and Alfred North Whitehead (1861-1974) in 1903 proposed the axiomatic set theory in a three-volume work called Principia Mathematicians find it awkward to digunakan.Sebuah axiomatic set theory can be done and logistics is fully given in 1908 by Ernst Zermello ( 1871 to 1953).wa was increased in 1921 by A. Fraenkel Ibrahim (1891-1965) and T. Skolem (1887-1963) and now known as' Zermello-Frankel (ZF)-axiomatic set theory.
Sources:
http://www-groups.dcs.st-and.ac.uk/ ~ history / HistTopics / Beginnings_of_set_theory.htmlhttp://en.wikipedia.org/wiki/Set_theoryhttp://www.mathresource.iitb.ac.in/project/history.htmhttp://stanford.library.usyd.edu.au/entries/set-theory/