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.

## Tags

adult algebra animations arithmetic astronomy biology books chemistry college computer science constructivism curriculum demonstrations earth science economics engineering enrichment programs essays events geometry grades 1-6 grades 4-12 grades 5-12 grades 5-Adult grades 9-Adult K-12 K-Adult linguistics logic math math circles math classes math education math problems online courses papers philosophy physics popular lectures preschool problem solving recreational math tools trigonometry videos