Uma investigação sobre a ideia de número
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Data
2020-12-18
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Universidade Federal de Goiás
Resumo
In this assignment we aim to stimulate reflections about the millenary inquiry regarding what
number really is. We aimed to show how historically controversial this question might be,
which finds diversified comprehensions in the fields of philosophy, mathematics and the
philosophy of mathematics. We came up with a historical pathway related to the construction
of the idea of number, since the paleolithic period, reaching the end of the Nineteenth Century,
when the mathematicians reevaluated the basics of mathematics and raised the ideas up to the
level of the most rigorous languages involving logic. Frege (1884), in his book "The
Fundamentals of Arithmetic", intended to explain and justify the real nature of the numbers
idea, without appealing to geometry. Besides him, we have put a spotlight on the beautiful ideas
as well as the important contributions of Bertrand Russell, Hilbert, Dedekind and Peano on the
construction of the idea of number. The rational approach of the concepts and their validation
through rational methods, without making use of sensorial experiments, are either philosophical
and mathematics studies. In this assignment, we intended to bring some light to these ideas,
acknowledging the relevance of a deeper and more structured comprehension of the idea of
number.
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Matemática, Número, Filosofia e lógica, Mathematics, Number, Philosophy and logic
Citação
SILVA, F. O. Uma investigação sobre a ideia de número. 2020. 71 f. Dissertação (Mestrado em Matemática em Rede Nacional) - Universidade Federal de Goiás, Catalão, 2020.