Introduction to the Hyperreals and Nonstandard Analysis

By Yitzchak Solomon

September 11, 2013

Abstract

Nonstandard analysis is a framework that allows us to make the notion of infinitesimals rigorous. This talk will be divided into three parts. In the first part, we will discuss the historical background behind infinitesimals, and the model-theoretic results that motivated the construction of nonstandard analysis. In the second part, we will construct the hyperreals again, this time as an analogue of the construction of the reals. Lastly, we will demonstrate what analysis looks like using infinitesimals, and (granted there is time) attempt to absolve Cauchy of a 250-year-old mistake.