What is infinity?

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Does infinity exist? Does it exist in the physical world or just in our heads? How many infinities are there? And are we allowed to do sums with them? Find out in these Plus articles.

Is the Universe finite or infinite? Is there infinity inside a black hole? Is space infinitely divisible or is there a shortest length? We talk to philosophers and physicists to find out.

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

Take a trip into the never-ending.

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.

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, ... .

John Barrow gives us an overview, from Aristotle's ideas to Cantor's never-ending tower of mathematical infinities, and from shock waves to black holes.