A complementaridade entre os aspectos intensional e extensional na conceituação de número real proposta por John Horton Conway - Fonseca, Rogério Ferreira da (2010)
This research is theoretical and has the goal of studying the concept of the real number. Epistemological issues are discussed surrounding the concept of number in general, and in particular the concept of real numbers. The discussions are based on the concept of complementarity as regards the analysis of cognitive and epistemological aspects of mathematical concepts. The focus of the research is to investigate a new proposal for the concept of numbers presented by the British mathematician John Horton Conway of Princeton University, which allows one to uniquely answer the question, What is a number? , which has long mobilized Mathematics philosophers and epistemologists. In addition, for this theory, a class of games is presented as a model for interpretation or application of the theory, thereby conceptualizing number as a game. Moreover, the game has assisted in learning Mathematics. We can conclude with this research that Conway s theory, in a complementary manner, can add new elements to the classical approaches to the concept of number, can indicate some of its weaknesses, and can highlight the importance of epistemological questioning in the evolution of mathematical knowledge. Another result of this research is to indicate the fertility of the concept of number that opens new frontiers for Mathematics. It is our opinion that Mathematics Education needs to be and should be close to advances in Mathematics