Title: R as a vector space over Q, with an interesting consequence

Speaker: Dustin Hedmark

Abstract: We will look at the real numbers as a vector space over the rational numbers. After reviewing relevant linear algebra terminology, we will show that this is an infinite dimensional vector space. Next, we will use the vector space R over Q to show that there does not exist a tiling of a rectangle of dimensions 1 by x with squares, where x is an irrational number.