Transreal numbers: Mathematics or Reverie?

This paper was presented and published, in Portuguese, in the symposium Os Números dos Mundos (The Numbers of the Worlds) in the 14º Seminário Nacional de História da Ciência e da Tecnologia (14th National Seminar on the History of Science and Technology) promoted by SBHC – Sociedade Brasileira de História da Ciência (Brazilian Society of History of Science) which took place on 08-11 October 2014, in Belo Horizonte, Minas Gerais, Brasil. The web page of the seminar is at http://www.14snhct.sbhc.org.br/ Original version is here: http://dx.doi.org/10.6084/m9.figshare.1254444