# Cauchy's real line and math philosophy till XIX

I have to write an essay concerning philosophy of mathematics until the end of XIX century. I've heard that the reason why the Cauchy's theorem (if continuous functions $fn→f$ then $f$ is continuous too) is wrong nowadays is the fact that his real numbers line (number system) was different then the modern one. It is indeed a very interesting topic but I couldn't find anything specific about it. Could you direct me to some sources or suggest a different topic?

• See Greg Graviton's answer at mathoverflow.net/questions/67879/…. The sense in which Cauchy's "real number line" is different is that he included infinitesimals when he did calculus. – KCd May 23 '16 at 22:03
• 1. Questions on homework assignment are not welcome on this site. 2. I would recommend you to read the work of Bolzano for the beginning of research on your topic. One modern work specifically related to your question is Imre Lakatos, Proofs and refutations, very last chapter. – Alexandre Eremenko May 25 '16 at 18:55