Mar 26, 2012
— read in fullInfinity Explained
Infinity is one of the most important ideas in maths – and one of the most confusing. Find out more about this mindbending idea.
It’s easy to think about infinity as if it is just a very, very big number – but it’s a lot stranger than that. If something is infinite, it is completely endless. For example, there are infinitely many – or an infinite amount of – numbers : whatever number you write down, you could always add one to it, or double it, because there is never a biggest number.
In fact, infinity comes in different sizes. For example, although there are infinitely many whole numbers and infinitely many numbers with decimal points, there are more of the second than there are of the first. This was shown by Georg Cantor in 1891 – and, unsurprisingly, sparked off a huge debate among mathematicians.
One famous way to think about the strange way that infinity behaves is the “Infinite Hotel”. Imagine a hotel with infinite rooms, and with a guest in every room. You might think that nobody new can stay at the hotel, but they can. If a new guest arrives, the hotel manager can move the person in room 1 into room 2, the person in room 2 into room 3, and so on forever, and the new guest can stay in room 1.
In fact, the “full” hotel can make room for an infinite number of new guests. If every guest moves into the room with double their current room number (so the person in room 1 moves into room 2, the person in room 2 moves into room 4, and so on) then all the odd-numbered rooms will be empty – and there are infinitely many odd numbers.
Of course, these ideas don’t fit into anything that we experience in our day-to-day lives. To understand infinity, you have to realise that it isn’t just a very big number, but a different idea altogether.
Related links
Your shout!
What do you think makes infinity so hard to understand? Share your thoughts by posting a comment using the link below.
