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Probability Theory by Raphael Tavares de Alencar, Marcelo Sampaio de Alencar

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         CHAPTER 1         

ADVANCED SET THEORY

An empty set is really full of nothing.

1.1  SET THEORY

The modern theory of sets was developed by the Prussian mathematician Georg Ferdinand Ludwig Philipp Cantor (1845–1918), in the end of the 19th century. After concluding his PhD under the supervision of the Polish mathematician, Leopold Kronecker (1823–1891), at the Humboldt University, in Germany, Cantor established the mathematical and logical basis for the theory and demonstrated several important results.

The mathematical concept of set cardinality and the notion of denumerable and nondenumerable sets, defined by Cantor, were fundamental to the modern theory of sets. Cantor was born in Saint Petersburg, but lived most of his academic life ...

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