## A Book of Set Theory (Dover Books on Mathematics) ebook rar

Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concerned with those that are relevant to mathematics as a whole.

The next wave of excitement in set theory came around 1900, when it was discovered that some interpretations of Cantorian set theory gave rise to several contradictions, called antinomies or paradoxes. Bertrand Russell and Ernst Zermelo independently found the simplest and best known paradox, now called Russell's paradox: consider \"the set of all sets that are not members of themselves\", which leads to a contradiction since it must be a member of itself and not a member of itself. In 1899, Cantor had himself posed the question \"What is the cardinal number of the set of all sets?\", and obtained a related paradox. Russell used his paradox as a theme in his 1903 review of con