Infinity is a topic that has for ages caused a great deal of both fascination and confusion among students. It is a mathematical abstraction that unlike other abstractions seems hard to make concrete. The fact there is more than one type of infinity and that infinity is often treated like a number but is not an element of what we know as the real numbers adds to the confusion. The charming little video below from the Open University takes a sixty second look at Hilbert’s paradox of the Grand Hotel, a comic, yet mathematically serious example of how to think about infinity. The name is a bit of a misnomer as it’s not really a paradox, but simply a question with a somewhat counterintuitive answer. The animation does not explore all aspects of Hilbert’s thought experiment, but it is a good start that will pique anyone’s curiosity.