Types of Infinity

Abstract

The concept of infinity pervades much of modern mathematics. Even elementary school students use the word infinity. However, what do we mean by infinity? While, for many infinity merely means either very large or not finite, in various contexts, the term infinity carries more information. Here we consider infinity in the contexts of cardinality (sizes of sets), ordinals (the order of numbers), and real numbers (a number system). Our aim is to introduce these various notions of infinity to interested mathematics students and whet their appetite for more. To accomplish this, we have included three online applets for readers to consider when teaching or learning about mappings from between natural and rational numbers.