What is infinity?

Podcast

Does infinity exist?

Find out how infinity can corrupt the youth, why subtracting infinities can give you the right answer, and the weirdness that might be lurking out there in the cosmos...
Article

Hilbert's hotel

How to squeeze infinitely many new guests into a full hotel.
Collection

What is infinity?

What is infinity? Does it even exist? And how many infinities are there?
Blog post

Maths in a minute: Counting numbers

Are there more irrational numbers than rational numbers, or more rational numbers than irrational numbers? Well, there are infinitely many of both, so the question doesn't make sense. It turns out, however, that the set of rational numbers is infinite in a very different way from the set of irrational numbers.
Podcast

Do infinities exist in nature? The podcast

Is the Universe finite or infinite? Is there infinity inside a black hole? Is space infinitely divisible or is there a shortest length? Can infinity occur at all in the cosmos or is it a mathematical construct? Find out more in our podcast with Anthony Aguirre, John D. Barrow and George Ellis.
Blog post

Maths in a minute: Countable infinities

An infinite set is called countable if you can count it. In other words, it's called countable if you can put its members into one-to-one correspondence with the natural numbers 1, 2, 3, ... .
Article

Phantasms of infinity

Infinity is a pain. Its paradoxes easily ensnare the unsuspecting reasoner. So over the centuries, mathematicians have carefully constructed bulwarks against its predations. But now cosmologists have developed theories that put them squarely outside the mathematicians' "green zone" of safety.
Podcast

Does infinity exist: the podcast

In the latest poll of our Science fiction, science fact project you told us that you wanted to know if infinity exists. In this interview the cosmologist John D. Barrow gives us an overview on the question, from Aristotle's ideas to Cantor's never-ending tower of mathematical infinities, and from shock waves to black holes.
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