Transfinite Numbers and Cardinal Arithmetic
DOI:
https://doi.org/10.31416/rsdv.v5i2.133Keywords:
Cantor, Set Theory, Transfinite Numbers, Cardinal ArithmeticAbstract
The Set Theory was developed in a rigorous and modern way in the late nineteenth century by Georg Cantor (1845-1918) to address certain subtle questions of function theory. Cantor's revolutionary ideas, at first misunderstood as too abstract for the time, were rapidly imposing themselves as unifying element of various branches of mathematics, to the point of becoming the means by which all contemporary mathematics is formalized. The applications of set theory to the solution of questions concerning the algebraic structure of various types of sets and questions concerning their operative properties opened new paths for mathematicians. The purpose of this
article was to promote a study of transfinite numbers using Cantor's theory, as well as to present the arithmetic of infinity - cardinal arithmetic. Preliminary results are presented in the general set theory and functions.
References
ALFONSO, A. B.; NASCIMENTO, M. C.; FEITOSA, H. A. Teoria dos Conjuntos: Sobre a Fundamentação Matemática e a Construção de Conjuntos Numéricos, Rio de Janeiro: Ed. Ciência Moderna Ltda., 2011.
ÁVILA, G. Várias Faces da Matemática, Segunda Edição, São Paulo: Blucher, 2010.
BOYER, C. B.. História da Matemática. Trad. Elza Gomide. São Paulo: Blucher, 1974.
HEFEZ, A. Curso de Álgebra, volume 1, Quarta Edição, Rio de Janeiro: IMPA, 2011.
LEVY, A. Basic Set Theory, Dover Publications, 2002.
SUPPES, P. Axiomatic Set Theory, New York: Dover Publications, 1977.
HEIN, N.; DADAM, F. Teoria Unificada dos Conjuntos, Rio de Janeiro: Editora Ciência Moderna, 2009.
ROCHA, J. Treze Viagens pelo Mundo da Matemática, Rio de Janeiro, SBM, 2012.
LIMA, E. L. Curso de Análise, vol. 1, Rio de Janeiro: IMPA, 2012.
NETO, A. C. M. Tópicos de Matemática Elementar: introdução à Análise, Rio de Janeiro: SBM, 2012.
