Hello, and welcome to the famous Hilbert Hotel, where our service and amenities have been drawing in countless guests since 1924. Are you here to check in? We currently have an infinite number of guests each staying in one of our infinite number of rooms. However, despite being at max capacity, we would be happy to move things around and open up a room for you. We hope you enjoy your stay!
Although intuition would tell us that it is impossible to check into a hotel with an infinite number of people in it, that is the magic of infinity. Even though the concept of infinity has been around for thousands of years, humans are not exactly the best at understanding its concepts. Whether it be in mathematics, physics, or even philosophy, the concept of infinity challenges our intuitions and deepens our understanding of the world around us. In this website, we will learn about the philosophers who discovered infinity, dive into how to properly think of infinity, and see how infinity affects us and our universe.
Before we dive into the history and applications of infinity, we should probably define exactly what “infinity” means. Although it might be the response you get when you ask a 3rd grader what the biggest number you can think of is, infinity is not a number. Famous mathematician Eugenia Cheng says so herself. Cheng says “Infinity is not a number but an idea—a way of talking about processes that never end rather than about things we can reach.” (Cheng, 2017) The concept of something that is endless, something that has no bounds seems really intuitive and simple, but the more you learn about infinity, the more complicated it becomes.