It is a challenge to define an uncountable set of real numbers that is dense in the real line and whose complement is also uncountable and dense. In this article we specify, for any positive integer k ...

The following dichotomy is established for any pair F, G of hereditary families of finite subsets of N: Given N, an infinite subset of N, there exists M an infinite subset of N so that either ...

For 50 years, mathematicians have believed that the total number of real numbers is unknowable. A new proof suggests otherwise. In October 2018, David Asperó was on holiday in Italy, gazing out a car ...