How Can Some Infinities Be Bigger Than Others?

The Joy of Why

The idea of infinity is probably about as old as numbers themselves, going back to whenever people first realized that they could keep counting forever. But even though we have a sign for infinity and can refer to the concept in casual conversation, infinity remains profoundly mysterious, even to mathematicians. In this episode, Steven Strogatz chats with his fellow mathematician Justin Moore of Cornell University about how one infinity can be bigger than another (and whether we can be sure that there isn’t an intermediate infinity between them). They also discuss how physicists and mathematicians use infinity differently and the importance of infinity to the very foundation of mathematics.