Abstract

Theory of sets (varieties) this one of the divisions of mathematics. In it they are studied the general properties sets are determined properties and characteristics, that possess what that general by property. Georg Cantor is considered the father of theory rightfully, which helped Richard Dedikind. The author of theory proposed the new concept of understanding nature of infinity, but the substantiation of theory itself is not entirely correct, which gave birth to logical contradictions both in theory itself and in those following, on its basis. The original form of the theory was later called the naive set theory. The monograph indicated in the list of literature provides a thorough analysis of set theory. At one time, set theory was severely criticized by well-known mathematicians: Henri Poincaré, Leutzen Weil and Hermann Weil, and even Cantor Richard Dedekind's associate. They asserted that to Cantor all put outting themselves of mathematics, considered urgent infinity not scientific concept and this was error. Scientific disputes apropos of naive set theory it does not cease up to now. In the article possible inaccuracies and even errors in the theory of Cantor's varieties are examined.