Transreal Arithmetic in History Book

Transreal arithmetic has made it into the history books. In chapter six of The Cult of Pythagorus: Math and Myths, University of Pitsburgh Press, 2013, author Alberto A. Martinez, puts transreal arithmetic into its historical context. On the positive side, he says that transreal arithmetic appears to be consistent and that it has attractive properties for computation. On the negative side, he says it is not accepted by mathematicians and has not been shown to have any practical advantage for physics.