URL: http://www.jonhoyle.com/MAASeaway/200804

Counter-Intuitive Results from the Hyper-reals, Jonathan Hoyle, MAA Seaway Section, April 12, 2008 1:30 PM Room CL208

[Slides (HTML)] [Slides (PDF)] [Paper (HTML)] [Paper (PDF)] [Slides of Paper Presentation] [Other MAA Seaway Spring 2008 sessions]



Spring 2008 Conference of the Mathematical Association of America Seaway Section, hosted by the Syracuse University Mathematics Department, April 11-12, 2008.



The set of Hyperreals *R is known to be an ordered field which is Dedekind incomplete, but how is this incompleteness manifested analytically? The purpose of this presentation is to explore this and other properties of *R and provide some interesting and counter-intuitive results deriving from it. Examples will include the demonstration of holes in *R, as well as proving its failure to be closed under countable additivity.


Link to online Presentation

Link to Infinitesimals in Modern Mathematics

Link to online Presentation of paper

Download Presentation introduction [PDF format, 1.6 MB]

Download Infinitesimals in Modern Mathematics [PDF format, 225K]


Link to Fall 2011 Seaway page on Forensic Mathematics and the World Trade Center Project

Link to Spring 2009 Seaway page on Introduction to Surreal Numbers

Link to Fall 2007 Seaway page on Infinitesimals in Modern Mathematics




For more information, contact me at jonhoyle@mac.com