Plus.Maths.org
infinity
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...
Playing with infinity can lead to surprising outcomes – find out how with a big bag of balls and some superpowers.
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.
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.
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, ... .
Does infinity exist? In the latest online poll of our Science fiction, science fact project you told us that you'd like an answer to this question. So we went to speak to cosmologist John D. Barrow to find out more. We also bring you a range of other Plus articles on the subject of infinity, as well as an article from FQXi who are our partners on this project. Happy reading!
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.
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.