Infinity and strange math

Infinity is not a very big number. It is the idea of something that never ends, and when mathematicians took it seriously they found a hotel that is full but always has room, sums that go on forever but add up to 1, and infinities of different sizes.

Step	Page	You will be able to
Play	Does it ever end?	Explain why there is no biggest number, and make a strip of paper with only one side
Explore	Hilbert's hotel	Compare the sizes of sets by pairing them up, and fit new guests into a full infinite hotel
Build	Zeno, limits and sums that never end	See how infinitely many pieces can add up to a finite amount, and turn repeating decimals into fractions
Master	Countable infinity	List the integers, the pairs of numbers and all the fractions, one after another
Beyond	Cantor's diagonal argument	Prove that the real numbers cannot be listed, and that there are infinitely many sizes of infinity